Twenty principles for good spreadsheet practice Second ed.docx

Twenty principles for
good spreadsheet practice
Second edition
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independent advice.
ISBN 978-1-78363-150-6
CONTENTS
PREFACE 01
WHY TWENTY PRINCIPLES? 02
THE TWENTY PRINCIPLES EXPLAINED AND
ILLUSTRATED 03
The spreadsheet’s business environment 04

Designing and building your spreadsheet 06
Spreadsheet risks and controls 13
Foreword by Mazars
Supported by
One year ago, ICAEW first published its Twenty principles for
good spreadsheet practice.
The principles were launched as a response to the increased
recognition of the risks and
waste caused by poor spreadsheet practice. We believe that
having a set of principles
developed by an independent and respected body represents an
important milestone
in addressing these issues. We have been actively involved in
the development of the
principles and are strong advocates of their wider adoption. We
are therefore delighted
that ICAEW is progressing this initiative by producing this
updated edition and taking the
time to consider how the principles are being used in practice.
The Mazars team works on building and reviewing spreadsheets
for a range of uses across
industry. Over the past year we have begun to use the principles
in a number of different
ways to help drive change, for example:
• as a benchmark to evaluate and improve models for our
clients; we find they provide an
excellent basis on which to recommend change in governance
and implementation of

modelling best practice; and
• to reinforce with clients the importance of adopting
spreadsheet standards, such as the
FAST Modelling Standard which we believe to be vital in order
to improve productivity
and reduce risk when using spreadsheets across their
organisations.
We have also taken an active role in helping promote the
principles more widely across
industry. As an example, when it comes to public procurement,
we can see that a
requirement for bidder financial models to be compliant with
the principles would be
much more useful than the current obligations, which look to
undefined notions of ’best
practice’. We have written about this in more detail in our blog
which is dedicated to
financial model review – themodelauditor.com.
If you haven’t already reviewed the principles, we urge you and
your teams to do so and
see whether you think that their adoption could help reduce the
amount of time wasted
and the potential for costly and embarrassing error in your
business.
After one year, the principles have begun to demonstrate their
worth in practice and
we believe that their wider promotion and adoption offers a real
opportunity to make
a step-change in industry practice. We wholeheartedly
recommend them to you.
Jerome Brice

Partner and Head of Model Audit
A
Like it or not, spreadsheets are in use everywhere. They have
become the
lingua franca of business; no matter what your system or
requirement,
a spreadsheet can connect people like no other business tool.
However, the use of spreadsheets is not without risk, and
approximately
90% of spreadsheets contain mistakes. Material errors such as
incorrect
models, sending out sheets with hidden columns or careless use
of
formulae, have been well publicised alongside the
embarrassment and
financial loss that arise as a result.
In addition, there is a serious problem of waste arising from
spreadsheets
that are created inefficiently or carelessly. 65% of members of
the Excel
Community are self-taught, and with no formal methodology
there is a
risk that sub-optimal models and processes become the norm.
This is why ICAEW’s Excel Community Advisory Committee
came together
to develop Twenty principles for good spreadsheet practice that
look to
reduce spreadsheet risk and inefficiency in all organisations
regardless of

size or sector.
I would like to thank all the members of the committee for
developing these
principles, and would encourage readers to act on the
recommendations in
this report.
Michael Izza
Chief Executive Officer, ICAEW
Preface
01Twenty principles for good spreadsheet practice
Many spreadsheets evolve over time without well-structured
design
or integrity checks, and are poorly documented. Making a
relatively
simple change can often take a long time, have unexpected
consequences and/or result in errors from incorrect calculations
or
input assumptions, as famously illustrated by debacles such as
the
bidding process for the West Coast mainline franchise.1
Why twenty principles?
The purpose of these principles is to
help reduce the amount of time wasted,
and the number of errors caused, by
businesses (including accountancy
practices) as a consequence of the
way they and their employees use

spreadsheets.
There are several points to emphasise.
First, no set of principles or standards
can guarantee freedom from error. The
design, maintenance and operation
of spreadsheets are still carried out by
humans.
Secondly, this document is not only about
‘good spreadsheet design’. The business
environment in which spreadsheets are
created, maintained and used is at least
as important. So the first four principles
are ones we believe should be adopted
by an organisation before anyone starts
to work on any individual spreadsheet-
using project. They are intended to create
a framework, and to instil attitudes,
which encourage best-practice to flourish.
These principles are addressed not only
to those directly involved in the design
and use of spreadsheets but also to those
with managerial responsibility, including
responsibility for management of risk.
They may also be of interest and relevance
to those with responsibility for audit.
Third, these are ‘principles’, not
‘standards’. By way of example, Principle
2 requires clarity and consistency in the
use of formatting. This could mean using
a particular cell colour to denote cells
allowing user input. There might be any
number of different corporate standards,
or publicly available standards, that adhere

to this principle. One standard might
specify pink as the colour for input cells;
another might specify green. Either would
satisfy the principle.
Finally, this set of principles is not meant
to be comprehensive, nor is it meant
to be very detailed. Deliberately it
focuses mainly on traditional formula-
driven spreadsheet construction, which
still accounts for the vast majority of
spreadsheet use, rather than on pivot
tables, structured references etc. It is a ‘top
20’ list, with each principle set out simply
and concisely, and with some explanation
and illustration added.2 It would of course
be possible to provide much more detail
than this, and to produce a much longer
document. These principles are intended
to be very widely applicable, and are
intended to cover projects of all shapes
and sizes and degrees of complexity. As
technology, and the ways people use it,
evolves, the priorities set out here may
need to change, and so the IT Faculty
intends to keep these principles under
regular review.
1In October 2012, at significant cost to the taxpayer, the
Department for Transport had to withdraw the
contract to run the West Coast Mainline rail service from the
company that had ‘won’, after it was discovered
that there had been errors in the way the bids had been assessed.
It was widely reported (for example
theguardian.com/politics/2012/oct/05/west-coast-civil-servant-
transport) that the spreadsheet used for the

calculations was seriously flawed.
2Excel 2013 is used for the illustrations. If you are using an
earlier version, some of the screenshots will look
different, and some features may not be available.
Twenty principles for good spreadsheet practice02
http://www.theguardian.com/politics/2012/oct/05/west-coast-
civil-servant-transport
The twenty principles
explained and illustrated
The spreadsheet’s
business environment
1. Determine what role spreadsheets play in your business, and
plan your spreadsheet standards and processes accordingly
If you have spreadsheets that play a key or critical role in your
organisation, ensure
that they are developed and tested, managed and monitored to
an appropriate level.
Spreadsheets that form part of an organisation’s key business
processes will need to be
managed differently from ad hoc spreadsheets for short-term use
by an individual.
2. Adopt a standard for your organisation and stick to it

This might be one that is developed in-house, or adopted from
outside and shared
with other organisations. A common standard within an
organisation facilitates
collaboration, aids understanding and saves development time.
The standard should
include, among other things, consistent conventions on use of
cell formatting.
This may be achieved by using the ‘cell styles’ feature as
illustrated below.
3. Ensure that everyone involved in the creation or use of
spreadsheets has an appropriate level of knowledge and
competence
For anyone designing, developing or maintaining (as distinct
from just using) a
spreadsheet, this will include: awareness of the range of
functions available, clear
understanding of such basic concepts as relative and absolute
cell references, and an
appreciation of the importance of carefully checking the results
of functions.
4. Work collaboratively, share ownership, peer review
The extent of collaboration and review needed will depend on
the size and complexity
of your organisation and of each project.
Trademark acknowledgements: Excel is a registered trademark
of Microsoft Inc. Screenshots reprinted by permission from
Microsoft Corporation.

Designing and building
your spreadsheet
5. Before starting, satisfy yourself that a spreadsheet is the
appropriate tool for the job
Spreadsheets are not the answer to every problem. A lot of time
can be wasted, and
errors caused, by using a spreadsheet when some other
application would be more
appropriate. Very often the more appropriate tool might be a
word processor (if it’s
a table of text), a database (if it’s processing large quantities of
similar data items) or
an existing software package (if it’s to undertake well-
established processes, such as
bookkeeping, for which specialist packages are readily
available). Even if a spreadsheet is
still the right answer it’s worth looking for existing templates
before starting a new one
from scratch.
6. Identify the audience. If a spreadsheet is intended to be
understood and used by others, the design should facilitate this
If the only ‘audience’ envisaged is yourself, you might perhaps
justify less explanation
and help. Even so, good documentation is helpful if you come
back to a spreadsheet a

while after you created it; and many spreadsheets come to have
a much wider audience
than originally intended. Ensure that adequate instructions,
validation and help are
included to promote ease of use and avoid input errors. Even if
parts of a spreadsheet
are ‘locked’, keep calculations visible.
7. Include an ‘About’ or ‘Welcome’ sheet to document
the spreadsheet
This should give such basic information as author, purpose,
version number, and
description of general approach. Also include explanations of
colour codes and other
formatting conventions, any sources of input data (with, where
appropriate, hyperlinks
to the original data), and any macros and what they do. The
more complex the
workbook, or the more it needs to be shared, the greater the
requirement for good
documentation. Conversely, a simple spreadsheet to be used
only by the person who
designs it might be less rigorously documented.
8. Design for longevity
Design spreadsheets to adapt to any reasonably foreseeable
future changes in values
(tax rates, etc) or volume (eg, items in a data set) of data used
in calculations. However,

the need for adaptability should be balanced against following
the Agile principle of
‘The simplest thing that could possibly work’.
In the first example above, if an organisation were to add a new
department, a new
worksheet could be added anywhere between DeptA and DeptD
(DeptC1, for instance),
and there would be no need to change the formula as the new
worksheet would
automatically be picked up by the formula. In the second
example above, the formula
would need to be changed every time a new worksheet is added.
9. Focus on the required outputs
Work backwards: be clear about the purpose of the spreadsheet,
what outputs achieve
that purpose and therefore what inputs and logic are required to
derive the outputs.
10. Separate and clearly identify inputs, workings and outputs
A properly structured spreadsheet will be easier to understand
and to maintain.
If pivot tables are used, it may be possible to relax this
principle, but clarity remains
crucial. Design to ensure that any input should be entered only
once.

11. Be consistent in structure
Use the same columns for the same things in each workbook,
especially when working
with time series. A consistent convention within a workbook
reduces the risk of error
where one sheet refers to another. For example, a common
convention is that time
flows horizontally from left to right (and a specific column is
always ‘Year 1’) and
calculations flow vertically from top to bottom. Such a structure
will help to avoid
circular references.
12. Be consistent in the use of formulae
On any worksheet use the smallest practicable number of
different formulae. Where
it is necessary to use different formulae, ensure that groups of
cells using the different
formulae are clearly separated.
In the left-hand example above, the formula =$A15*B$11 in
cell B15 has been copied
across and down to all the cells in the range B15:D24, whereas
in the right-hand
example, because the $ sign was not used, a formula had to be
entered manually into
each of the 30 cells in turn. This significantly increased the risk
of error and the time
needed to review the worksheet. ‘Go To Special’ – ‘Column
differences’ is an error-
checking process looking for inconsistencies. In the left-hand
example it generates the
message ‘No cells were found’, meaning that there are no
inconsistent formulae; in the
right-hand example cells K16:K24 remain highlighted, showing
that the formulae in that

range are different from the one used in K15 at the top of the
column.
13. Keep formulae as short and simple as practicable
Shorter formulae are easier to build (and therefore less likely to
contain errors) and easier
to understand and to review. Stage a calculation through
multiple cells rather than build
a long, complex formula.
14. Never embed in a formula anything that might change or
need to be changed
Instead, put such values into separate cells and reference them.
This ensures that values
enter the spreadsheet only once, and if change is needed would
happen in just one
place. It also allows for all formulae cells to be locked without
denying access to input
values.
In the left-hand example above, the VAT amounts in B15:B24
and E15:E24 have been
calculated by a formula and the cells in those ranges have been
locked and the sheet
protected (which is why clicking into one of them produces the
message displayed). In
the right-hand example, the formulae in the equivalent cells
included the VAT rate as a
figure rather than as a reference to a cell containing the rate. In
this example, if the VAT
rate were to change, each formula containing the VAT rate as a
figure would need to

be identified and changed manually – running the risk of
introducing errors in the rate
entered or in the actual formula. Additionally, in the right-hand
example the formulae
were not protected, and they appear to have been manually
overwritten by mostly
wrong values.
15. Perform a calculation once and then refer back to that
calculation
Do not calculate the same value in multiple places (except
perhaps for cross checking
purposes). This reduces risk of error, and is more efficient,
since fewer calculations are
being performed.
16. Avoid using advanced features where simpler features
could
achieve the same result
In particular, avoid using programming code unless necessary –
in which case ensure
that it is clearly documented within the code itself, as well as in
a documentation
worksheet. Similarly, avoid circular references, and control and
document any
exceptions. Do not change the software’s key default settings
(for example, do not turn
off automatic recalculation) unless essential, in which case
include a prominent message
to warn users.

Spreadsheet risks
and controls
17. Have a system of backup and version control, which should
be
applied consistently within an organisation
The appropriate levels of backup and version control will
depend on the organisation
and the nature of the work, but there should always be, at the
very least, a reliable
means of preserving, identifying and restoring earlier versions
of a workbook.
18. Rigorously test the workbook
The level of testing required will depend on the size,
complexity and criticality of the
workbook, with riskier workbooks needing a greater degree of
independent testing.
This example illustrates the use of ‘trace precedents’, which
shows all the cells

which affect the value of the currently selected cell and ‘trace
dependents’, which
shows all the cells containing formulae that refer to the active
cell.
19. Build in checks, controls and alerts from the outset and
during
the course of spreadsheet design
These checks might include, for example, tests to ensure that a
balance sheet balances,
assets do not depreciate below zero, and so on. One approach
would be to build in a
set of audit tests to check validity and use flags to signal
compliance or non-compliance.
Use a master flag to summarise all the individual flags and
place it prominently (on the
output sheet, or even throughout the workbook eg, on sheet
headers) so that users are
bound to see it.
In the second of the two examples above, the actual interest rate
that has been input
is 12%, which is 2% above the upper limit – hence the warning
‘red spots’ and the
explanatory error message.
20. Protect parts of the workbook that are not supposed to be

changed by users
The level of protection will vary according to the nature of the
spreadsheet and the kind of
use/users it will have. It might include locking whole
worksheets, all cells containing formulae,
or everything except designated input cells.
Acknowledgments
Twenty principles for good spreadsheet practice is the result of
debate among members of the
IT Faculty’s Excel Community Advisory Committee, who saw
the document through a number
of drafts over several months, and then took on board comments
from the wider ICAEW
membership and the public. The members of the Excel
Community Advisory Committee
were as follows:
Christopher Blunn Grace Frank
Tom Brichieri-Colombi Mazars
Roland Brook Smith & Williamson
Grenville Croll EuSpRIG
Daniel Emkes Harrow School
Glen Feechan needaspreadsheet.com
Simon Hurst The Knowledge Base
Alistair Hynd Baker Tilly
Tony Lee Global Aerospace
David Lyford-Smith BDO
Adrian Maconick Finsbury

Solution
s
Sanjay Magecha Financial Visibility
Vinit Patel Filtered
Rishi Sapra KPMG
John Tennent Corporate Edge
Paul Wakefield Paul Wakefield
Dave White White Bruce
Recognition of spreadsheet standards
The IT Faculty has developed a scheme
whereby spreadsheet standards, and other
products and services such as training,
can be formally recognised as compliant
with the Twenty Principles.
So far, the following products have
achieved recognition:
• The FAST Modelling Standard

• FinRobot’s Base, Topline, Case Builder and
Manufacturing standard models
• Best Practice Spreadsheet Modelling
Standards and bpmToolbox software
SPREADSHEET
PRINCIPLES
COMPLIANT
The twenty principles in brief
The spreadsheet’s business environment
1. Determine what role spreadsheets play in your business,
and plan your
spreadsheet standards and processes accordingly.
2. Adopt a standard for your organisation and stick to it.

3. Ensure that everyone involved in the creation or use of
spreadsheets has
an appropriate level of knowledge and competence.
4. Work collaboratively, share ownership, peer review.
Designing and building your spreadsheet
5. Before starting, satisfy yourself that a spreadsheet is the
appropriate
tool for the job.
6. Identify the audience. If a spreadsheet is intended to be
understood
and used by others, the design should facilitate this.
7. Include an ‘About’ or ‘Welcome’ sheet to document the
spreadsheet.
8. Design for longevity.
9. Focus on the required outputs.
10. Separate and clearly identify inputs, workings and outputs.

11. Be consistent in structure.
12. Be consistent in the use of formulae.
13. Keep formulae as short and simple as practicable.
14. Never embed in a formula anything that might change or
need to be
changed.
15. Perform a calculation once and then refer back to that
calculation.
16. Avoid using advanced features where simpler features
could achieve the
same result.
Spreadsheet risks and controls
17. Have a system of backup and version control, which
should be applied
consistently within an organisation.
18. Rigorously test the workbook.

19. Build in checks, controls and alerts from the outset and
during the
course of spreadsheet design.
20. Protect parts of the workbook that are not supposed to be
changed
by users.
!
© ICAEW 2015 TECPLM13983 06/15
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specialising in audit, advisory, accounting and tax services. The
Group
operates in 73 countries and draws on the expertise of 15,000
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Mazars’ specialist financial modelling team has a wealth of
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infrastructure finance and its skills are increasingly called on
for a wide

range of corporate applications. The team is recognised as a
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teams from our offices in London, Paris, New York and Delhi.
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Excel is one of the most popular end-user tools in the
accountant’s portfolio.
Spreadsheets enable us to quickly and flexibly perform analysis
that otherwise
would be difficult or time-consuming; however, there is a
tendency to place
undue trust in them. ICAEW’s Excel Community provides a
‘one-stop shop’
for accountants who want to use Excel better and understand
and minimise
spreadsheet risk.
For more information about the Excel Community, please visit
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Peer Review
1. Read your peer’s essay from beginning to end just to let its
ideas wash over you. What are your initial thoughts? Did your
peer satisfy the requirements of assignment? Please explain in
detail.

I think the peer’s essay does not cover what the question
requires it to. In this essay the peer does not satisfy the
requirements of the assignment as the writer ends up describing
the different sources of renewable energy and even the statistics
on how they are used instead of describing why people should
use renewable sources of energy.
2. Review the essay’s title as well as its introduction and
conclusion. Think about the relationships among these three
components. Do they match or do they disagree? Make note of
strengths or weaknesses in these crucial areas. Please explain
in detail.
The introduction is well set but has a weakness as it goes out of
topic when the peer begins to give details about the non-
renewable sources which were not part of the assignment’s
requirement. Apart from that, there is a clear relationship
between the title, introduction and conclusion as they all base
on the reasons why renewable energy sources are preferable.

3. Find the essay’s thesis. Is it clear? Is it well positioned?
Paraphrase (put in your own words) the thesis of the essay to
check your understanding. Review the assignment guidelines to
ensure that your peer’s thesis is on target. Make note of
strengths or weaknesses in this area. Please explain in detail.
The essay’s thesis is clear and well positioned at the end of the
introduction. My thesis would be ‘my goal in this paper is to
explain why people should prefer using renewable energy as
their main source of energy’
According to the assignment details; the peer was supposed to
give reasons as to why people should prefer using renewable
energy sources which is covered in the thesis though not
directly.
The peer’s thesis is giving us the clear position that the peer
was supposed to support throughout the essay.
4. Focus on the individual paragraphs of the essay. Does each
paragraph have a topic sentence that previews the ideas of the

paragraph? Observe the essay’s development of paragraphs.
Does each paragraph have a single main idea that relates to the
thesis? Are there any paragraphs that seem disconnected or out
of place?
Although some of the paragraphs have the topic sentence, most
of the paragraphs do not have the main idea. This is because the
peer ended up describing the renewable sources of energy, how
they work and statistics of how they are used instead of
elaborating on the reasons why renewable energy should be
preferable.
5. Consider the essay’s use of the English language. Are
sentence structures, grammar, spelling, punctuation and
mechanics employed effectively, or do errors distract the reader
from understanding and enjoying the writer’s analysis? Make
note of strengths and weaknesses in this area. Please explain in
detail.
Apart from just few grammar mistakes, the writer’s sentence

structures are good, the spelling is also efficient, punctuations
and mechanics are also employed effectively.
The few errors made do not affect the enjoyment and
understanding of the writers analysis as the points are well
structured.
Remember: When in doubt about how to do the peer review, be
honest, helpful, and constructive. Saying “Great job! Don’t
change a word!” never helped anyone to be a better writer.
Last Name 6
Mays Almudallal
William Matter
ENGL-1301-83420
03-05-2018
Renewable Energy is the way to go
Huge amounts of energy are used to power automobiles,
factories, electrical appliances, and other modern life features

in the United States and other countries where mechanization is
the order of the day. Renewable energy and fossil fuels are two
key sources of energy for these processes. Katrin Jordan-Korte
defines renewable energy as “energy that is derived from
natural processes that are replenished constantly. In its various
forms, it derives directly or indirectly from the sun, or from
heat generated deep within the earth” (11). Non-renewable
energy sources, on the other hand, are depleted once they are
mined from the earth and burned. Examples of substances
comprising non-renewable energy include natural gas, oil, and
coal, all of which are formed as a result of matter that has
decayed over millions of years. Opponents of renewable energy
argue that sources of nonrenewable energy are well established,
hence they are capable of supplying energy at low costs
compared to renewable sources. There is need for the critics to
focus on the positive aspects of renewable energy and note the
diversity of its sources including solar, biomass, hydropower,
wind, and geothermal energy.
Proponents of renewable energy argue that the global supply of
non-renewable energy is restricted and will be ultimately
depleted. Thus, they assert that development of renewable
sources of energy is the only way to create a reliable and secure
energy solution for the generations to come. Burning of fossil
fuels emit greenhouse gases such as carbon dioxide, causing
greenhouse effect and air pollution, and cause climate change.

Hydropower is one of the most prevalent source of renewable
energy (in 2016, it accounted for 6.5 percent of total energy
produced in the United States) (U.S. Department of Energy a 3).
Globally, hydropower accounts for a whopping 71 percent of the
total renewable energy generated and about 16.4 percent of the
power produced from all the sources. This energy is harnessed
through flowing water in big rivers. In a characteristic
hydropower plant, pipes are used to channel water that flows
through a dam to turn huge turbines thus generating power.
Hydropower, just like other sources of renewable energy, does
not pollute the environment. In addition to aiding in the
generation of clean energy, dams can also be used to manage
freshwater resources and control floods.
Wind is another source of clean energy. Kinetic energy
produced by wind is captured through massive turbines and then
converted into electricity. After production, the energy is then
supplied to the power grid by the utility firms. In the United
States, there is an upwards of 15,000 GW of energy that can be
generated from wind, both offshore and land-based (U.S.
Department of Energy b 2). Wind power has several economic
and environmental advantages. Being a renewable and clean
source of energy, wind power supports public health and helps
to maintain quality of air.
Biomass energy is a form of renewable energy that is derived
mostly from plants. Plants accumulate energy from the sun

which can then be emitted through burning. The energy in
biomass is usually obtained by transforming the biomass into
gas or liquid biofuel fuel. Alternatively, the energy can be
obtained by combusting it to produce electricity or heat. The
most popular sources of biomass include agricultural
byproducts, wood waste, as well as solid wastes from the
municipal. In the year 2015, power produced from biomass
accounted for about 1.6 percent of the total amount of
electricity produced in the United States (U.S. Department of
Energy a 4).
One of the most frequently produced biofuel is ethanol. This
type of fuel is as a result of the sugars found in farm products
such as corn, potatoes, sugar cane, rice, and wheat. Ethanol is
often mixed with gasoline and used in the transport sector.
Close to 13.2 billion million gallons of ethanol were produced
in 2010 alone in the United States. This accounts for roughly 87
percent of the world’s total ethanol supply (Renewable Fuels
Association 10).
Solar energy is a type of renewable energy that occurs as solar
radiation from the sun. This radiation is then directly or
indirectly transformed into power or other forms of usable
energy. In his article published by Greentech Media, Mike
Munsell observes that “In total, solar accounted for 39 percent
of new capacity additions across all fuel types in 2016”. Two
key techniques which are used to produce electricity from solar

radiation are known as photovoltaic and thermal. The latter
technic uses the rays from the sun to turn liquid into steam,
which is then used to generate power while the former method
directly transforms sun rays into power directly. These methods
can be used either in large or small scale to produce energy for
the national grid or additional power for use in schools, homes,
and businesses.
Geothermal power is generated using the heat that is formed
under the earth’s crust. When water infiltrates into the ground
and comes into contact with molten rocks within the earth’s
crust, it becomes hot and forms steam that can be used to
harness electricity or can be used directly. Geothermal power is
produced and used in many parts of the world where there are
active volcanoes, or where tectonic plates converge. Parts of the
world such as Iceland have geothermal energy as their main
source of energy (accounting for over 25 percent of the total
electricity produced). This form of energy generation are also
widespread in several states in the western half of the U.S
including Nevada, California, and Alaska. About 90 percent of
installed geothermal power capacity is in California (Sifford
and Bloomquist 441).
Those who oppose the use of renewable energy claim that
entities dealing in fossil fuels are deeply established and have
the ability to supply power at cheaper rates. Further, they argue
that if too much focus is put in generating energy from

renewable sources, there will be loss of jobs in the firms
producing energy through fossil fuels. However, it is estimated
that the rate of job creation in the renewable energy sector is
higher than that is the non-renewable sector. In addition,
investing in renewable energy brings other benefits such as
protection of the environment.
Other critics are of the opinion that renewable energy is too
expensive to generate in terms of the machinery and the skills
required. Such people, therefore, contend that generation of
energy from renewable sources is not feasible. The truth is that
the initial investment required to start a plant to generate energy
from renewable sources is very high. However, the fact that the
industry is rapidly growing and the technology is advancing
really fast means that the process will be cost effective with
time.
A section of environmentalists have come out to disapprove
hydropower, claiming that it negatively affects the immediate
natural environment. According to them, constructing
hydroelectric dams significantly changes the ecosystem of the
river. Further, they argue that such water reservoirs leads to the
displacement of humans, animals, and threatens plant life.
Nevertheless, these effects are not anything compared to the
environmental degradation caused by use of fossil fuels to
generate energy. Further, measures are being taken when
constructing dams to ensure least disruption is caused in the

process and that displaced people are fairly compensated or
relocated.
Renewable energy has the potential of providing the world with
most of its energy solutions. This type of energy has a great
advantage over nonrenewable energy; the ability to be used
without being exhausted. This, together with other benefits such
as being harmless to the environment, and the fact that it can be
harnessed from a range of sources (solar, biomass, hydropower,
wind, and geothermal energy), makes renewable energy a
superior option of power generation.

Works Cited
Jordan-Korte, Katrin. Government Promotion of Renewable
Energy Technologies: Policy Approaches and Market
Development in Germany, the United States, and Japan. Berlin,
Germany: Springer Science & Business Media, 2011. Web.
Renewable Fuels Association. "Acelerating Industry Innovation
- 2012 Ethanol Industry Outlook." 6 March 2012. Renewable
Fuels Association. Web. 5 March 2018.
Sifford, Alex and R. Gordon Bloomquist. "Geothermal Electric
Power Production In The United States:." Proceedings World
Geothermal Congress (2000): 441-454. Web.
U.S. Department of Energy. "U.S. Hydropower Market Report
2017 Update (April)." April 2017. U.S. Department of Energy.
Web. 5 March 2018.
—. "WindVision: A New Era for Wind Power in the United
States." 2014. U.S. Department of Energy. Web. 5 March 2018.
INFO 1010
MULTI VARIABLE
MEASURES OF VARIABILITY

‹#›
1
Measures of Association
Between Two Variables
Thus far we have examined numerical methods used
to summarize the data for one variable at a time.
Often a manager or decision maker is interested in
the relationship between two variables.
Two descriptive measures of the relationship
between two variables are covariance and correlation
coefficient.
‹#›
Covariance
Positive values indicate a positive relationship.

Negative values indicate a negative relationship.
The covariance is a measure of the linear association
between two variables.
‹#›
Covariance
The covariance is computed as follows:
for
samples
for
populations

=
=
‹#›
Correlation Coefficient
Just because two variables are highly correlated, it
does not mean that one variable is the cause of the
other.
Correlation is a measure of linear association and not
necessarily causation.
‹#›
The correlation coefficient is computed as follows:

for
samples
for
populations
=
=
‹#›
Values near +1 indicate a strong positive linear
relationship.
Values near -1 indicate a strong negative linear

relationship.
The coefficient can take on values between -1 and +1.
The closer the correlation is to zero, the weaker the
relationship.
‹#›
Sample Covariance
Sample Correlation Coefficient
Covariance and Correlation Coefficient
Example: Golfing Study
= = = -7.08
=
‹#›
Using Excel to Compute the

Excel Formula Worksheet
A
B
C
D
1
Average
Drive

18-Hole
Score
2
277.6
69
Samp. Covariance
=COVARIANCE.S(A2:A7,B2:B7)
3
259.5
71
Samp. Correlation
=CORREL(A2:A7,B2:B7)
4
269.1
70
5
267.0
70
6
255.6
71
7
272.9
69
8

‹#›
Using Excel to Compute the
Excel Value Worksheet
A

B
C
D
1
Average
Drive
18-Hole
Score
2
277.6
69
Samp. Covariance
-7.08
3
259.5
71
Samp. Correlation
-0.9631
4
269.1
70
5
267.0
70
6

‹#›
INFO 1010
SINGLE VARIABLE MEASURES OF VARIABILITY
‹#›
1
Measures of Variability
It is often desirable to consider measures of variability

(dispersion), as well as measures of location.
For example, in choosing supplier A or supplier B we might
consider not only the average delivery time for each, but also
the variability in delivery time for each.
‹#›
Measures of Variability
Range
Interquartile Range
Variance
Standard Deviation
Coefficient of Variation
‹#›
Interquartile Range
The interquartile range of a data set is the difference between
the third quartile and the first quartile.
It is the range for the middle 50% of the data.

It overcomes the sensitivity to extreme data values.
‹#›

525
530
530
535
535
535
535
535
540
540
540
540
540
545
545
545
545
545

550
550
550
550
550
550
550
560
560
560
565
565
565
570
570
572
575
575
575
580
580
580
580
585
590

590
590
600
600
600
600
610
610
615
625
625
625
635
649
650
670
670
675
675
680
690
700
700
700
700

Interquartile Range
3rd Quartile (Q3) = 625
1st Quartile (Q1) = 545
IQR = Q3 - Q1 = 625 - 545 = 80

‹#›
Variance
The variance is a measure of variability that utilizes all the
data.
It is based on the difference between the value of each
observation (xi) and the mean ( for a sample, m for a
population).
The variance is useful in comparing the variability of two or
more variables.
=VAR.S(data cell range)
‹#›
Standard Deviation
The standard deviation of a data set is the positive square root

of the variance.
It is measured in the same units as the data, making it more
easily interpreted than the variance.
STDEV.S(data cell range)
‹#›
Standard
deviation is
about 9%
of the mean
Variance
Standard Deviation
Coefficient of Variation
Sample Variance, Standard Deviation,
And Coefficient of Variation
Apartment Rents
s2 = = 2,996.16
s =

% =
‹#›
Measures of Distribution
Distribution Shape
z-Scores
Chebyshev’s Theorem
Empirical Rule
Detecting Outliers
‹#›
Distribution Shape: Skewness
An important measure of the shape of a distribution is called
skewness.
The formula for the skewness of sample data is

Skewness =
‹#›
Symmetric (not skewed)
Relative Frequency

.05
.10
.15
.20
.25
.30
.35
0
Skewness = 0
Skewness is zero.
Mean and median are equal.
‹#›

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Moderately Skewed Left
Skewness = - .31
Skewness is negative.

Mean will usually be less than the median.
‹#›
Moderately Skewed Right
Relative Frequency
.05
.10
.15
.20
.25

.30
.35
0
Skewness = .31
Skewness is positive.
Mean will usually be more than the median.
‹#›
Highly Skewed Right

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = 1.25

Skewness is positive (often above 1.0).
‹#›
Seventy efficiency apartments were randomly
sampled in a college town. The monthly rent prices
for the apartments are listed below in ascending order.
Example: Apartment Rents

525
530
530
535
535
535
535
535
540
540

540
540
540
545
545
545
545
545
550
550
550
550
550
550
550
560
560
560
565
565
565
570
570
572
575

575
575
580
580
580
580
585
590
590
590
600
600
600
600
610
610
615
625
625
625
635
649
650
670
670

675
675
680
690
700
700
700
700
715
715

‹#›
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0

Skewness = .92
‹#›
Empirical Rule

When the data are believed to approximate a
bell-shaped distribution …
The empirical rule is based on the normal
distribution, which is covered in Chapter 6.
The empirical rule can be used to determine the
percentage of data values that must be within a
specified number of standard deviations of the
mean.
‹#›
Empirical Rule
For data having a bell-shaped distribution:
of the values of a normal random variable
are within of its mean.
68.26%
+/- 1 standard deviation
95.44%
+/- 2 standard deviations

99.72%
+/- 3 standard deviations
‹#›
Empirical Rule
x
m – 3s
m – 1s
m – 2s
m + 1s
m + 2s
m + 3s

m
68.26%
95.44%
99.72%
‹#›
z-Scores
Standardized Values for Apartment Rents

‹#›
The z-score is often called the standardized value.
It denotes the number of standard deviations a data
value xi is from the mean.
z-Scores
Excel’s STANDARDIZE function can be used to
compute the z-score.
=
‹#›
z-Scores
A data value less than the sample mean will have a
z-score less than zero.
A data value greater than the sample mean will have

a z-score greater than zero.
A data value equal to the sample mean will have a
z-score of zero.
An observation’s z-score is a measure of the relative
location of the observation in a data set.
‹#›
Z-Scores and Distributions
‹#›
Detecting Outliers
An outlier is an unusually small or unusually large
value in a data set.
A data value with a z-score less than -3 or greater
than +3 might be considered an outlier.
It might be:
an incorrectly recorded data value
a data value that was incorrectly included in the

data set
a correctly recorded data value that belongs in
the data set
‹#›
Chebyshev’s Theorem
At least (1 - 1/z2) of the items in any data set will be within z
standard
deviations of the mean, where z is any value greater than 1.
Chebyshev’s theorem requires z > 1, but z need not be an
integer.
At least of the data values must be
within of the mean.
75%
z = 2 standard deviations
within of the mean.
89%
within of the mean.

94%
‹#›
Five-Number Summaries
and Box Plots
Summary statistics and easy-to-draw graphs can be
used to quickly summarize large quantities of data.
Two tools that accomplish this are five-number
summaries and box plots.
‹#›
Five-Number Summary
1
Smallest Value
First Quartile
Median

Third Quartile
Largest Value
2
3
4
5
‹#›
Box Plot
A box plot is a graphical summary of data that is
based on a five-number summary.
A key to the development of a box plot is the
computation of the median and the quartiles Q1 and
Q3.
Box plots provide another way to identify outliers.
‹#›

Box Plot
Whiskers (dashed lines) are drawn from the ends of the box to
the smallest and largest data values
inside the limits.
500
525
550
575
600
625
650
675
700

725
Smallest value
inside limits = 525
Largest value
inside limits = 715
‹#›
Data Dashboards:
Adding Numerical Measures
to Improve Effectiveness
The addition of numerical measures, such as the mean
and standard deviation of KPIs, to a data dashboard

is often critical.
Drilling down refers to functionality in interactive
dashboards that allows the user to access information
and analyses at increasingly detailed level.
Dashboards are often interactive.
Data dashboards are not limited to graphical displays.
‹#›
‹#›
-1.20
-1.11
-1.11
-1.02
-1.02
-1.02
-1.02

-1.02
-0.93
-0.93
-0.93
-0.93
-0.93
-0.84
-0.84
-0.84
-0.84
-0.84
-0.75
-0.75
-0.75
-0.75
-0.75
-0.75
-0.75
-0.56
-0.56
-0.56
-0.47
-0.47
-0.47
-0.38

-0.38
-0.34
-0.29
-0.29
-0.29
-0.20
-0.20
-0.20
-0.20
-0.11
-0.01
-0.01
-0.01
0.17
0.17
0.17
0.17
0.35
0.35
0.44
0.62
0.62
0.62
0.81
1.06

1.08
1.45
1.45
1.54
1.54
1.63
1.81
1.99
1.99
1.99
1.99
2.27
2.27
INFO 1010
CHARTS AND DESCRIPTIVE STATISTICS
‹#›
1

Joe’s Diner Example
Guests eating at Joe’s Diner were asked to rate the
quality of their meal as being excellent,
above average, average, below average, or poor. The
ratings provided by a sample of 20 customers are:
Below Average
Above Average
Above Average
Average
Above Average
Average
Above Average
Average
Above Average
Below Average
Poor
Excellent
Above Average
Average
Above Average
Above Average
Below Average
Poor
Above Average

Average
Frequency Distribution
‹#›
Frequency Distribution
Poor
Below Average
Average
Above Average
Excellent
2
3
5
9
1
Total 20
Rating
Frequency

‹#›
Using Excel’s COUNTIF Function
to Construct a Frequency Distribution
‹#›
Using Excel’s COUNTIF Function
to Construct a Frequency Distribution
‹#›

Relative Frequency and
Percent Frequency Distributions
Poor
Below Average
Average
Above Average
Excellent
.10
.15
.25
.45
.05
Total 1.00
10
15
25
45
5
100
Relative
Frequency
Percent
Frequency

Rating
.10(100) = 10
1/20 = .05
‹#›
Using Excel to Construct Relative Frequency and Percent
Frequency Distributions
‹#›
Using Excel to Construct Relative Frequency and Percent
Frequency Distributions

‹#›
Poor
Below
Average
Average
Above
Average
Excellent
Frequency
Rating
Bar Chart

‹#›
Histogram
Another common graphical display of quantitative data is a
histogram.
The variable of interest is placed on the horizontal axis.
A rectangle is drawn above each class interval with its height
corresponding to the interval’s frequency, relative frequency, or
percent frequency.
Unlike a bar graph, a histogram has no natural separation
between rectangles of adjacent classes.

‹#›
Histogram
Days on Market for Home Sales

2
4
6
8
10
12
14
16
18
Frequency
10-19 20-29 30-39 40-49 50-59 60-69

When the Format Data Series dialog box appears Set the Gap
Width to 0
‹#›
Symmetric
Histograms Showing Skewness

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Left tail is the mirror image of the right tail
Examples: Heights of People
‹#›

A longer tail to the left
Example: Exam Scores
Relative Frequency
.05
.10
.15
.20
.25
.30

.35
0
‹#›
Moderately Right Skewed
A Longer tail to the right
Example: Housing Values

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
‹#›
Highly Skewed Right
A very long tail to the right
Example: Executive Salaries

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0

‹#›
An important measure of the shape of a distribution is called
skewness.
The formula for the skewness of sample data is
Skewness =
‹#›
Symmetric (not skewed)

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = 0
Skewness is zero.
Mean and median are equal.
‹#›

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0

Skewness = - .31
Skewness is negative.
Mean will usually be less than the median.
‹#›
Moderately Skewed Right

Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0
Skewness = .31
Skewness is positive.
‹#›

Highly Skewed Right
Relative Frequency
.05
.10
.15
.20
.25
.30
.35
0

Skewness = 1.25
Skewness is positive (often above 1.0).
‹#›
Seventy efficiency apartments were randomly
sampled in a college town. The monthly rent prices
for the apartments are listed below in ascending order.

530
535
535
535
535
535
540
540
540
540
540
545
545
545
545
545
550
550
550
550
550
550
550
560
560

560
565
565
565
570
570
572
575
575
575
580
580
580
580
585
590
590
590
600
600
600
600
610
610
615

625
625
625
635
649
650
670
670
675
675
680
690
700
700
700
700
715
715

.05
.10
.15
.20
.25
.30
.35
0
Skewness = .92

‹#›
A
B
C
D
1
Quality Rating
Quality Rating
Frequency
2
Above Average
Poor
=COUNTIF($A$2:$A$21,C2)
3
Below Average
Below Average
4
Above Average
Average

5
Average
Above Average
6
Average
Excellent
7
Above Average
Total
=SUM(D2:D6)
8
Above Average
A
B
C
D
1
Quality Rating
Quality Rating
Frequency
2
Above Average

Poor
2
3
Below Average
Below Average
3
4
Above Average
Average
5
5
Average
Above Average
9
6
Average
Excellent
1
7
Above Average
Total
20
8
Above Average

C
D
E
F
1
Quality Rating
Frequency
Relative
Frequency
Percent
Frequency
2
Poor
=D2/$D$7
=E2*100
3
Below Average
=D3/$D$7
=E3*100
4
Average
=D4/$D$7

=E4*100
5
Above Average
=D5/$D$7
=E5*100
6
Excellent
=D6/$D$7
=E6*100
7
Total
=SUM(D2:D6)
=SUM(E2:E6)
=SUM(F2:F6)
8
C
D
E
F
1
Quality Rating
Frequency

Relative
Frequency
Percent
Frequency
2
Poor
2
0.10
10
3
Below Average
3
0.15
15
4
Average
5
0.25
25
5
Above Average
9
0.45
45
6

Excellent
1
0.05
5
7
Total
20
1.00
100
8
INFO 1010
SINGLE VARIABLE
CENTRAL TENDENCY MEASURES
‹#›
1
Measures of Location
If the measures are computed

for data from a sample, they
are called sample statistics.
If the measures are computed for
data from a population, they are
called population parameters.
A sample statistic is referred to as
the point estimator of the
corresponding population parameter.
Mean
Median
Mode
Percentiles
Quartiles
Weighted Mean
Geometric Mean
‹#›
Sample Mean

Number of
observations
in the sample
Sum of the values
of the n observations
‹#›
Population Mean m
Number of
observations in
the population
Sum of the values
of the N observations

‹#›
Weighted Mean
Denominator:
sum of the
weights
Numerator:
sum of the weighted
data values

If data is from
a population,
m replaces .
where:
xi = value of observation i
wi = weight for observation i
‹#›
Geometric Mean
= [(x1)(x2)…(xn)]1/n
Excel’s geometric mean function is:
=GEOMEAN(data cell range)
‹#›

Excel Formula Worksheet
Using Excel to Compute
the Mean, Median, and Mode
A
B
C
D
E
1
Apart-
ment

Monthly
Rent ($)
2
1
545
Mean
=AVERAGE(B2:B71)
3
2
715
Median
=MEDIAN(B2:B71)
4
3
530
Mode
=MODE.SNGL(B2:B71)
5
4
690
6
5
535

Percentiles
A percentile provides information about how the data are spread
over the interval from the smallest value to the largest value.
Admission test scores for colleges and universities are
frequently reported in terms of percentiles.
The pth percentile of a data set is a value such that at least p
percent of the items take on this value or less and at least (100 -
p) percent of the items take on this value or more.
PERCENTILE.EXC(data range, p/100)
‹#›
Quartiles
Quartiles are specific percentiles.
First Quartile = 25th Percentile
Second Quartile = 50th Percentile = Median
Third Quartile = 75th Percentile
QUARTILE.EXC (data range, quartile number)

‹#›
INFO 1010
MULTI VARIABLE DESCRIPTIVE STATISTICS
AND CHARTS
‹#›
1
Scatterplot: Summarizing Data for Two Variables Using
Graphical Displays
Crosstabulation: Summarizing Data for Two Variables Using
Tables
Data Visualization: Best Practices in Creating Effective
Graphical Displays

‹#›
Price
Range
French Italian Duplex Appt
Total
< $250,000
> $250,000
18 6 19 12
55
45
30 20 35 15
Total
100
12 14 16 3
Home Style
Crosstabulation

Example: Daniel’s Homes
The number of homes sold for each style and price for the past
two years is shown below.
quantitative
variable
categorical
variable
‹#›
A scatter diagram is a graphical presentation of the relationship
between two quantitative variables.
One variable is shown on the horizontal axis and the other
variable is shown on the vertical axis.
The general pattern of the plotted points suggests the overall
relationship between the variables.
A trendline provides an approximation of the relationship.
Scatter Diagram and Trendline

‹#›
Scatter Diagram
Positive Trend
x
y

‹#›
Scatter Diagram
Negative Relationship
x
y

‹#›
Scatter Diagram
No Apparent Relationship
x

y
‹#›
1
3
2
1
3
14
24
18
17
30
x = Number of
Interceptions
y = Number of
Points Scored
Scatter Diagram

The Broncos football team is interested in
investigating the relationship, if any, between
interceptions made and points scored.
‹#›
Scatter Diagram and Trendline
y
x

Number of Interceptions
Number of Points Scored
5
10
15
20
25
30
0
35

1
2
3
0
4
‹#›
INFO 1010
DATA MANAGEMENT AND ANALYSIS
‹#›
1

General Stat Concepts
Statistics
Descriptive Statistics
Statistical Inferences
Sample vs. Population
Problem:
Data Deluge
Data Quality
1st Step
Determine Scales of Measurement of Variables
‹#›
Scales Of Measurement
Scales determine the amount of information in the data
Nominal
Ordinal
Interval
Ratio

‹#›
Quantitative vs Categorical
Categorical: Labels or names used to identify an attribute of
each element. Can be numeric or nonnumeric
Quantitative: Indicates how much or how many. Always
numeric. Can be discrete or continuous.
The statistical analysis that is appropriate depends on whether
the data for the variable are categorical or quantitative.
In general, there are more alternatives for statistical analysis
when the data are quantitative.
‹#›
Scales of Measurement
Categorical
Quantitative
Numeric
Numeric
Non-numeric
Data

Nominal
Ordinal
Nominal
Ordinal
Interval
Ratio
‹#›
Statistical Inference
Population
Sample
Statistical inference
Census
Sample survey
- the set of all elements of interest in a
particular study
- a subset of the population
- the process of using data obtained
from a sample to make estimates
and test hypotheses about the

characteristics of a population
- collecting data for the entire population
- collecting data for a sample
‹#›
Process of Statistical Inference
1. Population
consists of all tune-
ups. Average cost of
parts is unknown.
2. A sample of 50
engine tune-ups
is examined.
The sample data
provide a sample

average parts cost
of $79 per tune-up.
4. The sample average
is used to estimate the
population average.
‹#›
Ethical Guidelines for Statistical Practice
In a statistical study, unethical behavior can take a
variety of forms including:
Improper sampling
Inappropriate analysis of the data
Development of misleading graphs
Use of inappropriate summary statistics
Biased interpretation of the statistical results
You should strive to be fair, thorough, objective, and
neutral as you collect, analyze, and present data.
As a consumer of statistics, you should also be aware

of the possibility of unethical behavior by others.
‹#›
Ethical Guidelines for Statistical Practice
The American Statistical Association developed the
report “Ethical Guidelines for Statistical Practice”.
Professionalism
Responsibilities to Funders, Clients, Employers
Responsibilities in Publications and Testimony
Responsibilities to Research Subjects
Responsibilities to Research Team Colleagues
The report contains 67 guidelines organized into
eight topic areas:
Responsibilities to Other Statisticians/Practitioners
Responsibilities Regarding Allegations of Misconduct
Responsibilities of Employers Including Organizations,
Individuals, Attorneys, or Other Clients
‹#›

This is for example only! Do NOT just copy this for your final
project!
This is for exam
ple only! Do NOT just copy this for your final project!
This is for example only! Do NOT just copy this for your final

project!
Optimization Rubric
Dashboard
DO NOT JUST COPY THE EXAMPLE DASHBOARD!!!
Unacceptable - 10 points
Acceptable – 20 points
Excellent - 30 points
· No dashboard
· Dashboard information is inaccurate
· Dashboard is basically a copy of the example.
· Missing a few of these things, or these are not clearly
described, or these are inaccurate, but overall acceptable
· Clear instructions on how to use the optimization created.
· Instructions on what things the Manager could change
· Instructions on how you created it
· Well organized, well labeled, easy to use, and easy to
understand
· Highlights important aspects
· Visually appealing

Part 1
Unacceptable – 20 points
(5 points each)
· No part 1
· Information is inaccurate
· Correct objective function
· Correct cost/profit calculations
· Correct constraints
· Correct boxes made
· Identifies how many boxes of each tea will be produced
· Identifies how much of each ingredient will be left over in
inventory
· Identifies the limiting factor(s)
· Gives suggestions to manager
· Worksheet has proper validation constraints
Part 2
Unacceptable – 20 points

(5 points each)
· No part 2
· Information is inaccurate
· Correct objective function
· Correct cost/profit calculations
· Correct constraints
· Correct boxes made
· Identifies how many boxes of each tea will be produced
· Identifies how much of each ingredient will be left over in
inventory
· Identifies the limiting factor(s)
· Gives suggestions to manager
· Worksheet has proper validation constraints
Writing
- 5 points for 1-2 typos or grammar problems
- 15 points for major editing concerns (i.e. it is hard to read past
the errors)
INFO 1010 Project 4
Due Friday, March 16 at 5:00 pm

HEAVENLY SPICES SPICE SHOP
Heavenly Spices makes a variety of Spice Mixes with a variety
of ingredients. They maintain a supply of various ingredients,
some of which are costlier than others. Each day, Heavenly
Spices mixes the appropriate ingredients for the varieties of
spice mixes they wish to make and packages the spice mixes in
their factory.
Some of their best-selling Spice Mixes are as shown in Table 1,
along with the chief ingredients for each spice mixes and the
amount of each ingredient.
Spice Mix Name
Ingredients (in grams) per spice mix box
Good Spice
5 gr Basil (BL)
17 gr Parsley (PA)
7 gr Thyme (TH)
8 gr Garlic Powder (GP)
4 gr Sage (SG)
2 gr Cloves (CL)
Market Pantry
18 gr Oregano (OR)
10 gr Basil (BL)
8 gr Sage (SG)
12 gr Thyme (TH)
Clear Your Sinuses

5 gr Black Pepper (BP)
10 gr White Pepper (WP)
18 gr Oregano (OR)
3 gr Parsley (PA)
16 gr Sea Salt (SS)
12 gr Marjoram Leaves (ML)
Sweetness
12 gr Cumin (CU)
15 gr Oregano (OR)
6 gr Cloves (CL)
8 gr Basil (BL)
3 gr Thyme (TH)
Palate’s Delight
6 gr Sage (SG)
6 gr Sea Salt (SS)
15 gr Marjoram Leaves (ML)
3 gr Chili Powder (CP)
Head Rush
7 gr Sea Salt (SS)
4 gr Parsley (PA)

8 gr Red Pepper (RP)
5 gr Ginger (GI)
6 gr Sage (SG)
Table 1: Spice Mixes
Each Spice Mix is packaged in a box that retails for $9.95 each.
While price is the same no matter the variety, the cost of
ingredients varies for each Spice Mix based on the type and
amounts of ingredients in each. Table 2 shows the per-gram
cost of each ingredient, and how much of each ingredient is in
stock and available for mixing:
Ingredient Name
Cost per gram in $
Availability in grams
Black Pepper (BP)
$0.12
9600
Basil (BL)
$0.18
13200
Parsley (PA)
$0.15
12500
Thyme (TH)
$0.21
9700

Garlic Powder (GP)
$0.15
6700
Sage (SG)
$0.09
9500
White Pepper (WP)
$0.12
12800
Oregano (OR)
$0.06
18400
Sea Salt (SS)
$0.09
5400
Cumin (CU)
$0.24
2700
Marjoram Leaves (ML)
$0.27
3500
Cloves (CL)
$0.18
5800
Chili Powder (CP)

$0.09
3000
Red Pepper (RP)
$0.21
6000
Ginger (GI)
$0.15
2000
Table 2: Herbal Ingredients
1. For inventory purposes, Heavenly Spices must produce at
least 125 boxes of each variety of Spice Mix. This holds for
both Parts 1 and 2.
Project Part 1:
A. Set up a Linear Programming model to maximize profit.
Identify the objective function and the formulas for all
constraints.
B. Run the model, and provide a copy of your answer report.
C. In a summary, identify how many boxes of each spice mixes
will be produced (does it make sense to make .65 of a box?) and
how much of each ingredient will be left over in inventory.
D. For each type of spice mix, identify the limiting factor(s)
which prevented Heavenly Spices from making more of that
spice mix.
Project Part 2:

A. With the exception of Market Pantry, Heavenly Spices is
able to sell no more than 400 boxes of each spice mixes.
Heavenly Spices is able to sell no more than 500 boxes of
Market Pantry. Re-run your model and provide a copy of your
answer report.
· Identify how many boxes of each spice mix will be produced
and how much of each ingredient will be left over in inventory.
B. Continuing with demand constraints above, maintenance
problems have limited today’s production to no more than 1600
units total. Re-run your model and provide a copy of your
answer report.
· Identify how many boxes of each spice mix will be produced
and how much of each ingredient will be left over in inventory.
Assignment Deliverables:
Create a spreadsheet that helps to answer these questions.
Create a tab for each Project Part and produce an answer report
within each tab. Clearly answer each question that is part of the
project. Most importantly, create a dashboard with instructions
on how to use the optimization you have created. It should have
instructions on what things you could change (Recipes? Costs?
Inventories? Other things?). It should have instructions on how
to maximize profits. It should be well organized, well labeled,
easy to use, and easy to understand.
3 of 3

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