The assignment part 2, section 1 writing sample the connection

1. The Assignment:
Part 2, Section 1: Writing Sample: The Connection Between
Academic and Professional Integrity
Using the Academic and Professional Success Development
Template you began in Week 1, write a 2- to 3-paragraph
analysis that includes the following:
· Explanation for the relationship between academic integrity
and writing
· Explanation for the relationship between professional
practices and scholarly ethics
· Cite at least two resources that support your arguments, being
sure to use proper APA formatting.
· Use Grammarly and SafeAssign to improve the product.
· Explain how Grammarly, Safe Assign, and paraphrasing
contributes to academic integrity.
Part 2, Section 2: Strategies for Maintaining Integrity of Work
Expand on your thoughts from Section 1 by identifying and
describing strategies you intend to pursue to maintain integrity
and ethics of your:
1. academic work as a student of the MSN program and
2. professional work as a nurse throughout your career. Include
a review of resources and approaches you propose to use as a
student and a professional.
Linear Equations
Central to algebra is the use of letters, most frequently x and y,
to represent numbers. Doing this allows us to deal
systematically with quantities that are unknown yet of
importance in an analysis. These unknown quantities are often
referred to as variables, literally things that vary over a range of
numbers or values. Sometimes the point is to express a
quantitative procedure in a succinct way, and the use of letters
merely constitutes convenient shorthand.

2. Example 1
A sales agent is paid a basic wage of £200 per week plus 10%
commission on sales. The procedure for working out his/her
total wage could be written as: 4
Total wage = 200 + 10% of sales
It is often more useful to abbreviate this by using letters. If y is
used to represent the total wage and x to represent sales we can
express the procedure as:
y = 200 + 0.1x
Using this we can find the total wage for a week when sales
were £1200:
y = 200 + 0.1 * 1200 = 200 + 120 = £320
Example 2
The sales agent in Example1, currently receiving a wage of
£200 plus 10% commission on sales, is offered the alternative
of receiving 20% commission on sales with no basic wage.
What is the minimum level of sales the agent would have to
reach to make the alternative commission-only wage attractive?
The existing arrangement can be represented as:
y = 200 + 0.1x
where y represents the wage and x the sales.
The alternative can be expressed as:
y = 0 + 0.2x
Both equations are plotted in Figure 1
Figure 1: The lines of the equations in Example 2
In Figure 1 the lines cross at the point representing sales of
£2000 and a wage of £400. The line representing the current
method of determining the wage is the higher line when sales
are below £2000, indicating that it would be the better
arrangement for the agent when sales are less than £2000. The
line representing the alternative arrangement is the higher line
when sales are greater than £2000, indicating that it would be
the better arrangement when sales exceed £2000. The minimum
level of sales the agent would have to reach to make the
alternative commission-only wage attractive is therefore £2000.

3. You can solve simultaneous equations without plotting their
lines on a graph using a method known as elimination. As the
name implies this involves removing or eliminating one of the
unknown quantities with the intention of leaving a numerical
value for the other.
In order to end up with a clear result conventionally
simultaneous equations are arranged so that the unknown
quantities and the factors applied to them, their coefficients, are
located on the left hand side of the equals sign and the
intercept, or constant appears to its right. This may involve
rearranging the equations. In doing this we need to ensure that
any manipulation preserves the equality inherent in the equation
by balancing every operation performed on one side with the
exact same operation on the other side.
Following this we proceed to the removal of one of the
unknown quantities, either x or y. This is straightforward if the
number of x’s or y’s in both equations is the same, in which
case if you subtract one equation from the other you will be left
with an expression which has just one unknown on the left of
the equals sign and a number on its right. Using suitable
multiplication or division you can then establish the value of
this remaining unknown, one of the pair of x and y values that
fits both equations.
Having found one of the pair of values mutually compatible
with both equations you can substitute it into one of the original
equations and find the value of the other unknown that, in
combination with the value of the first unknown, satisfies the
original equations jointly, or simultaneously.
Example 3
In Example 1 the sales agent is presented with two possible
wage arrangements represented as:
y = 200 + 0.1x (the original arrangement)
y = 0 + 0.2x (the alternative arrangement)
where y represents the wage and x the sales.
We will start by rearranging both equations so the components,
or terms, involving x and y are on the left of the equals sign and

4. the ‘stand-alone’ numbers are on the right. In the case of the
first equation, representing the original arrangement, this
entails moving the 0.1x from the right of the equals sign over to
the left. In doing this we have to reverse the sign in front of it,
as strictly speaking we are subtracting 0.1x from both sides of
the equation, and hence preserving the balance:
y = 200 + 0.1x
Subtract 0.1x from both sides:
y – 0.1x = 200 + 0.1x – 0.1x
to get:
y – 0.1x = 200
For the second equation:
y = 0 + 0.2x
Subtract 0.2x from both sides:
y – 0.2x = 0 + 0.2x – 0.2x
to get:
y – 0.2x = 0
We can now set these rearranged equations alongside each
another and subtract one from the other to eliminate y:
Y – 0.1x = 200
Y – 0.2x = 0
+0.1x = 200
This tells us that one-tenth of x is 200.
If we multiply both sides of this by ten we find that a ‘whole’ x
is worth 2000:
0.1x * 10 = 200 * 10 so 1x = 2000
In other words both wage determination models produce the
same wage when sales are £2000.
But what will the wage be? To find this put the sales figure of
2000 into the equation representing the original arrangement:
y = 200 + 0.1 * 2000 = 200 + 200 = 400
The original approach to establishing the sales agent’s wage
will produce a wage of £400 when sales are £2000. The
alternative, commission-only formulation will of course yield
the same wage when sales are £2000:
y = 0 + 0.2 * 2000 = 400

5. The values of 2000 and 400 for sales and wages respectively
therefore satisfy both wage determination equations
simultaneously. Applying elimination in Example 3 was made
easier because in both equations there was only one ‘y’, that is
the coefficient on y in each equation was one. If the coefficients
on an unknown are different you have to apply multiplication or
division to one or both equations to make the coefficients on the
unknown you wish to eliminate equal before you can use
subtraction to remove it.
Example 4
Find the level of wages at which the two procedures for
determining the sales agent’s wage in Example 2 result in the
same wage by eliminating x, the level of sales. The equations
representing the procedure, as rearranged in Example 3, are:
y = 200 + 0.1x (the original arrangement)
y = 0 + 0.2x (the alternative arrangement)
If we multiply the first equation by two we get:
2y – 0.2x = 400
Subtracting the second equation from this:
2Y – 0.2x = 400
Y – 0.2x = 0
Y = 400
Again we find that the wage level at which the two wage
determination models produce the same result is £400. If we
substitute this value of y into the equation representing the
original arrangement we can find the level of sales that will
yield a wage of £400:
400 – 0.1x = 200
Subtract 400 from both sides:
400 – 400 – 0.1x = 200 – 400
-0.1x = -200
Multiply both sides by minus one:
(-1) *-0.1x = -200 * (-1)
0.1x = 200

6. Multiply both sides by ten:
x = 2000
The level of sales at which both approaches to wage
determination will produce a wage of £400 is therefore £2000.
Not all pairs of equations can be solved simultaneously. These
are either cases where one equation is a multiple of another,
such as: 3x + 2y = 10 and 6x + 4y = 20 or cases where one
equation is inconsistent with the other, such as: 2x + y = 14 and
2x + y = 20 In the first case the equations are the same; if you
try to plot them you will find they produce the same line. In the
second case plotting them produces lines that are parallel and
therefore do not cross.
Break-Even Analysis
The type of linear model that we have looked at in the previous
section can be used to analyse the relationship between the
costs and revenue of a company. The aim in doing this is to
identify the point at which the revenue matches the costs,
known as the break-even point, the output level at which the
company makes neither profit nor loss but breaks even.
In setting up a break-even analysis we need to make several
definitions and assumptions. First we assume that there are two
types of cost, fixed and variable. Fixed costs, as the name
implies, are those costs that are constant whatever the level of
production. These might be the costs of setting up the operation
such as the purchase of machinery as well as expenses, such as
business rates, that do not vary with the level of output.
Variable costs on the other hand are costs that change in
relation to the amount produced, such as the costs of raw
materials and labour. We can define the total costs (TC) as the
sum of the total fixed costs (TFC) and the total variable costs
(TVC):
TC = TFC + TVC
The total variable costs depend on the quantity of output. We
will assume that the variable cost of producing an extra unit is
the same however many units we produce; in other words, it is
linear or varies in a straight line with the amount produced. We

7. can therefore express the total variable cost as the variable cost
per unit produced, known as the average variable cost (AVC)
multiplied by the quantity produced (Q), so the total cost is:
TC = TFC + AVC * Q
The total revenue (TR) is the price per unit (P) at which the
output is sold multiplied by the quantity of output (Q):
TR = P * Q
Once we have defined the total cost and total revenue equations
we can plot them on a graph and look at exactly how total
revenue compares to total cost. This is a key comparison as the
total revenue minus the total cost is the amount of profit made:
Profit = TR – TC
The point at which the lines representing the two equations
cross is the point at which total cost is precisely equal to total
revenue, the break-even point.
Example 5
The Ackrana Security Company intends to manufacture video
security cameras. The costs of acquiring the necessary plant and
machinery and meeting other fixed costs are put at £4.5 million.
The average variable cost of producing one of their cameras is
estimated to be £60 and the company plans to sell them at £150
each. How many will they need to produce and sell in order to
break even?
Total cost, TC = 4,500,000 + 60Q
Total Revenue. TR = 150Q
These equations are plotted in Figure 2. Conventionally the
money amounts, cost and revenue are plotted on the vertical or
y axis and the output is plotted on the horizontal or x axis. This
arrangement reflects the assumption that the money amounts
depend on the output and makes it easier to interpret the
diagram.
Figure 2
Total cost and total revenue lines in Example 5
In Figure 5 the steeper line that starts from the origin represents

8. the total revenue equation and the other line represents the total
cost equation. You can see that the lines cross when output is
about 50,000 units. At this level of production both the total
cost and total revenue are equal, at about £7.5 million. This is
the break-even point, at which costs precisely match revenues.
We can verify the break-even point by solving the total cost and
total revenue equations simultaneously:
Total cost, TC = 4,500,000 + 60Q so TC-
60Q = 4,500,000
Total Revenue. TR = 150Q so TR – 150Q = 0
When total cost and total revenue are equal, subtracting one
from the other will leave us with an expression in which the
only unknown is the level of output, Q:
TC- 60Q = 4,500,000
TR – 150Q = 0
+90Q = 4,500,000
Dividing both sides by 90 means that the level of output at
which total cost and total revenue are equal is 50,000:
4500000/90 = 50000
The total cost and total revenue when 50000 units are produced
will be:
TC = 4,500,000 + 60*50,000 = 4,500,000 + 3,000,000 =
7,500,000
TR = 150 * 50,000 = 7,500,000
Break-even analysis can be extended to illustrate the levels of
output that will yield a loss and those that will yield a profit. A
level of output less than the break-even level, and hence to the
left of the position of the break-even point along the horizontal
axis of the graph, will result in a loss. A level of output higher
than the break-even level, to the right of the break-even point
on the horizontal axis, will yield a profit.
At any point to the left of the break-even point the total cost
line is the higher line indicating that total cost is higher than

9. total revenue; the greater the difference between the two lines,
the larger the loss. At any point to the right of the break-even
point the total revenue is the higher line, which means that the
total revenue is higher than the total cost; the bigger the
difference between the two lines, the larger the profit. The areas
representing loss and profit are shown in Figure 3.
Figure 3
Break-even graph for Example 5 with areas representing profit
and loss
Using Figure 3 you can establish how much profit or loss will
be achieved at a particular level of production. If for instance
production were 30,000 units the graph suggests that the total
cost would be £6.3 million and the total revenue would be £4.5
million resulting in a loss of £1.8 million.
We expect that a company would seek to operate at a level of
production at which they would make a profit. The difference
between the output they intend to produce, their budgeted
output, and the break-even level of output is their safety
margin. This can be expressed as a percentage of the budgeted
output to give a measure of the extent to which they can fall
short of their budgeted output before making a loss.
Example 6
If the Ackrana Security Company in Example 5 aims to produce
80,000 cameras what profit should they expect and what is their
safety margin?
TR = 150 * 80,000 = 12,000,000
TC = 4,500,000 + 60*80,000 = 9,300,000
Profit = 12,000,000 – 9,300,000 = 2,700,000
In Example 5 we found that their break-even point was 50,000
cameras so their safety margin is:
Budgeted output – break-even output * 100 = 80000-50000*100
= 37.5%

10. Budgeted output
80000
The break-even analysis we have considered is the simplest
case, where both costs and revenue are assumed to be linear,
that is to form straight lines when plotted graphically. In
practice companies might find that with greater levels of
production come economies of scale that mean their variable
cost per unit is not constant for every unit produced but falls as
output increases. Furthermore, they may have to reduce their
price if they want to sell more products so that their total
revenue would not have a linear relationship to their output
level.
Despite these shortcomings the basic model can be a useful
guide to the consequences of relatively modest changes in
output as well as a framework for considering different levels of
initial investment, pricing strategies and alternative sources of
raw materials.
Questions:
1. The current system for allocating budgets for the local
depots of a national office-cleaning company gives each depot a
fixed sum of £35,000 plus an extra £500 for each corporate
client in the area the depot covers.
(a) Express the budget allocation model as an equation.
(b) Use your equation from (a) to work out the budget
allocations for the following depots:
(i) Ashford, which has 43 corporate clients
(ii) Byfleet, which has 29 corporate clients
(iii) Croydon, which has 66 corporate clients
(c) A new accountant at the company head office wants to alter
the budget allocation model by reducing the fixed sum to
£20,000 and increasing to £800 the extra for each corporate
client. What changes will these alterations mean for the depots
in (b)?
2. A domestic consumer is offered two alternative methods of
paying for her annual water bill. The first option is to make 8

11. payments of £32 at certain points over the forthcoming year.
The second is to have her water metered and pay £0.08 for each
cubic metre of water used plus an annual standing charge of
£20. What is the maximum amount of water she would have to
use over the year to make it economical for her to choose the
second payment method?
3. Following a crash, the owner of the Skorrost Courier
Service has to purchase a new van. The make and model have
already been decided, but there is a choice between petrol and
diesel versions. The petrol version costs £10,000 to buy and
will incur fuel costs of £0.12 per mile. The diesel version costs
£11,000 and will incur fuel costs of £0.08 per mile. What is the
minimum number of miles that the vehicle must travel to make
purchasing the diesel version the more economical choice?
4 The Pasuda Porcelain Company is about to launch a new
luxury tableware range. The selling price for a set will be £90.
To make the range the company has invested £319,000 in new
equipment. Variable production costs will be £35 per set.
(a) What number of sets must they sell to break even?
(b) What profit will they make if they sell 6000 sets, and what
is their margin of safety?
5. Samocat Automotive want to move the production of their
motor scooters to a purpose-built new plant that will cost £24 m
to construct. The scooters sell for £1850 and variable costs of
production amount to £1100 per scooter.
(a) What is the break-even point for scooter production at the
new plant?
(b) How will the break-even point change if the costs of the
new plant rise to £30 m?
6. A plant hire company purchases a mobile crane for
£120,000. It plans to charge £190 a day for hiring out the crane.
For each day on which it is hired out the company expects to
incur variable costs of £40.
(a) Work out how many days the company needs to hire out the
crane in order to break even.
(b) If the variable costs are actually £55 and the hire charge

12. has to be reduced to £180 per day, what is the new breakeven
point?
7. Holly buys a hot dog stall for £360. In addition she has to
pay a fixed charge of £200 to the local council to secure her
pitch. She plans to sell her hot dogs at £1 each and the cost of
preparing each one is £0.60.
(a) How many hot dogs will she need to sell to break even?
(b) She finds a supplier that can provide cheaper hot dog
sausages, enabling her to save 10 p per hot dog on the
preparation cost. What effect does this have on the break-even
point?
8. Volna Appliances want to take over a competitor that
makes microwave ovens. They have bid £48 m for the company
and expect their offer to be accepted. The microwave ovens are
sold for £85 and variable costs amount to £25 per unit.
(a) Work out the break-even point for microwave production.
(b) Volna plan to introduce a rationalization plan that will
reduce variable costs by £6 and a price reduction of £16 to
increase market share. What is the new break-even point?
Content represents a modification of Chapter 2, sections 2.2 and
2.3 of Buglear, John. Quantitative Methods for Business (pp.
74-76). Taylor and Francis.