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MAT 540 Final Exam (20 Sets)
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This Tutorial contains 20 Sets of Final Exam (800 Questions/Answers)
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MAT 540 Midterm Exam (5 Sets)
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This Tutorial contains 5 Sets of Midterm Exam
MAT 540 Midterm Exam Set 1
Question 1 Deterministic techniques assume that no uncertainty
exists in model parameters.
Question 2 A joint probability is the probability that two or more
events that are mutually exclusive can occur simultaneously.
Question 3 A continuous random variable may assume only integer
values within a given interval.
Question 4 A decision tree is a diagram consisting of circles decision
nodes, square probability nodes, and branches.
Question 5 Simulation results will always equal analytical results if
30 trials of the simulation have been conducted.

Question 6 Excel can only be used to simulate systems that can be
represented by continuous random variables.
Question 7 Data cannot exhibit both trend and cyclical patterns.
Question 8 The Delphi develops a consensus forecast about what
will occur in the future.
Question 9 In Bayesian analysis, additional information is used to
alter the __________ probability of the occurrence of an event.
Question 10 __________ is a measure of dispersion of random
variable values about the expected value.
Question 11 The __________ is the maximum amount a decision
maker would pay for additional information.
Question 12 Developing the cumulative probability distribution helps
to determine
Question 13 A seed value is a(n)

Question 14 Pseudorandom numbers exhibit __________ in order to
be considered truly random.
Question 15 Consider the following frequency of demand:
If the simulation begins with 0.8102, the simulated value for demand
would be
Question 16 __________ is a linear regression model relating
demand to time.
Question 17 worth 2 points, 1 hour time limit (chapters 1,ue units
EXCEPT:The U.S. Department of Agriculture estimates that the yearly
yield of limes per acre is distributed as follows:
Yield, bushels per acre Probability
350 .10
400 .18
450 .50
500 .22

The estimated average price per bushel is $16.80.
What is the expected yield of the crop?
Question 18 __________ methods are the most common type of
forecasting method for the long-term strategic planning process.
Question 19 In exponential smoothing, the closer alpha is to
__________, the greater the reaction to the most recent demand.
Question 20 Given the following data on the number of pints of ice
cream sold at a local ice cream store for a 6-period time frame:
If the forecast for period 5 is equal to 275, use exponential smoothing
with α = .40 to compute a forecast for period 7.
Question 21

Question 22 Coefficient of determination is the percentage of the
variation in the __________ variable that results from the __________
variable.
Question 23 Which of the following possible values of alpha would
cause exponential smoothing to respond the most slowly to sudden
changes in forecast errors?
Question 24 Consider the following demand and forecast.
Period Demand Forecast
1 7 10
2 12 15
3 18 20
4 22
If MAD = 2, what is the forecast for period 4?

Question 25 An automotive center keeps tracks of customer
complaints received each week. The probability distribution for
complaints can be represented as a table or a graph, both shown
below. The random variable xi represents the number of complaints,
and p(xi) is the probability of receiving xi complaints.
xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07
What is the average number of complaints received per week? Round
your answer to two places after the decimal.
Question 26 An online sweepstakes has the following payoffs and
probabilities. Each person is limited to one entry.
The probability of winning at least $1,000.00 is ________.
Question 27 A fair die is rolled 8 times. What is the probability that
an even number (2,4, 6) will occur between 2 and 4 times? Round your
answer to four places after the decimal.

Question 28 A life insurance company wants to estimate their annual
payouts. Assume that the probability distribution of the lifetimes of the
participants is approximately a normal distribution with a mean of 68
years and a standard deviation of 4 years. What proportion of the plan
recipients would receive payments beyond age 75? Round your answer
to four places after the decimal.
Question 29 The local operations manager for the IRS must decide
whether to hire 1, 2, or 3 temporary workers. He estimates that net
revenues will vary with how well taxpayers comply with the new tax
code. The following payoff table is given in thousands of dollars (e.g. 50
= $50,000).
If he uses the maximin criterion, how many new workers will he hire?
Question 30 An investor is considering 4 different opportunities, A, B,
C, or D. The payoff for each opportunity will depend on the economic
conditions, represented in the payoff table below.
Economic Condition

Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
If the probabilities of each economic condition are 0.5, 0.1, 0.35, and
0.05 respectively, what is the highest expected payoff?
Question 31 A normal distribution has a mean of 500 and a standard
deviation of 50. A manager wants to simulate one value from this
distribution, and has drawn the number 1.4 randomly. What is the
simulated value?
Question 32 Consider the following annual sales data for 2001-2008.
Calculate the correlation coefficient . Use four significant digits after
the decimal.

Question 33 The following data summarizes the historical demand for a
product.
Use exponential smoothing with α = .2 and the smoothed forecast for
July is 32. Determine the smoothed forecast for August.
Question 34 Robert wants to know if there is a relation between
money spent on gambling and winnings.
What is the coefficient of determination? Note: please report your
answer with 2 places after the decimal point.
Compute a 3-period moving average for period 6. Use two places after
the decimal.

Question 36 Given the following data, compute the MAD for the
forecast.
the decimal.
Question 38 The following sales data are available for 2003-2008 :
Calculate the absolute value of the average error. Use three significant
digits after the decimal.
Question 39 The following data summarizes the historical demand for
a product
If the forecasted demand for June, July and August is 32, 38 and 42,
respectively, what is MAPD? Write your answer in decimal form and

not in percentages. For example, 15% should be written as 0.15. Use
three significant digits after the decimal.
Question 40 This is the data from the last 4 weeks:
Use the equation of the regression line to forecast the increased sales
for when the number of ads is 10.
Question 1 Deterministic techniques assume that no uncertainty exists
in model parameters.

Question 3 An inspector correctly identifies defective products 90% of
the time. For the next 10 products, the probability that he makes fewer
than 2 incorrect inspections is 0.736.
Question 5 Starting conditions have no impact on the validity of a
simulation model.
Question 8 Qualitative methods are the least common type of
Question 9 __________ is a measure of dispersion of random variable
values about the expected value.

Question 10 In Bayesian analysis, additional information is used to alter
the __________ probability of the occurrence of an event.
Question 11 The __________ is the expected value of the regret for
each decision.
to determine
Question 13 A seed value is a(n)
Question 14 In the Monte Carlo process, values for a random variable
are generated by __________ a probability distribution.
Question 15 Two hundred simulation runs were completed using the
probability of a machine breakdown from the table below. The average
number of breakdowns from the simulation trials was 1.93 with a
standard deviation of 0.20.

Question 16 In exponential smoothing, the closer alpha is to
__________, the greater the reaction to the most recent demand.
Question 17 __________ is absolute error as a percentage of demand.
Question 18 __________ is a category of statistical techniques that
uses historical data to predict future behavior.
Question 19 Worth 2 points, 1 hour time limit (chapters 1,ue units
EXCEPT:The U.S. Department of Agriculture estimates that the yearly
yield of limes per acre is distributed as follows:
The estimated average price per bushel is $16.80.
What is the expected yield of the crop?
Question 20 __________ is a linear regression model relating demand
to time.

Question 21 Which of the following possible values of alpha would
cause exponential smoothing to respond the most slowly to sudden
changes in forecast errors?
Question 23 __________ is the difference between the forecast and
actual demand.
Question 25 A loaf of bread is normally distributed with a mean of 22
oz and a standard deviation of 0.5 oz. What is the probability that a loaf
is larger than 21 oz? Round your answer to four places after the
decimal.
Question 26 An online sweepstakes has the following payoffs and
probabilities. Each person is limited to one entry.
The probability of winning at least $1,000.00 is ________.

Question 27 A fair die is rolled 8 times. What is the probability that an
even number (2,4, 6) will occur between 2 and 4 times? Round your
answer to four places after the decimal.
Question 28 A life insurance company wants to estimate their annual
payouts. Assume that the probability distribution of the lifetimes of the
participants is approximately a normal distribution with a mean of 68
years and a standard deviation of 4 years. What proportion of the plan
recipients would receive payments beyond age 75? Round your answer
to four places after the decimal.
Question 29 An investor is considering 4 different opportunities, A, B,
C, or D. The payoff for each opportunity will depend on the economic
conditions, represented in the payoff table below.
If the probabilities of each economic condition are 0.5, 0.1, 0.35, and
0.05 respectively, what is the highest expected payoff?
Question 30 The local operations manager for the IRS must decide
whether to hire 1, 2, or 3 temporary workers. He estimates that net
revenues will vary with how well taxpayers comply with the new tax
code. The following payoff table is given in thousands of dollars (e.g. 50
= $50,000).

If he thinks the chances of low, medium, and high compliance are 20%,
30%, and 50% respectively, what is the expected value of perfect
information? Note: Please express your answer as a whole number in
thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole
number, if necessary.
Question 31 Given the following random number ranges and the
following random number sequence: 62, 13, 25, 40, 86, 93, determine
the average demand for the following distribution of demand.
product
product.
Use exponential smoothing with α = .2 and the smoothed forecast for
July is 32. Determine the smoothed forecast for August.

Question 34 Daily highs in Sacramento for the past week (from least to
most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast
for today using a 2 day moving average.
Question 35 Robert wants to know if there is a relation between money
spent on gambling and winnings.
Question 36 This is the data from the last 4 weeks:
Use the equation of the regression line to forecast the increased sales
for when the number of ads is 10.
Question 37 Daily highs in Sacramento for the past week (from least to
most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast
for today using a weighted moving average, with weights of .6, .3 and
.1, where the highest weights are applied to the most recent data.

forecast.
Year Demand Forecast
the decimal.
the decimal.

Question 2 An inspector correctly identifies defective products 90%
of the time. For the next 10 products, the probability that he makes
fewer than 2 incorrect inspections is 0.736.
Question 3 A continuous random variable may assume only integer
values within a given interval.
Question 6 A table of random numbers must be normally
distributed and efficiently generated.

Question 9 In Bayesian analysis, additional information is used to
alter the __________ probability of the occurrence of an event.
Question 10 __________ is a measure of dispersion of random
variable values about the expected value.
Question 11 The __________ is the maximum amount a decision
maker would pay for additional information.
Question 12 Pseudorandom numbers exhibit __________ in order to
be considered truly random.
to determine
Question 14 Consider the following frequency of demand:

If the simulation begins with 0.8102, the simulated value for demand
would be
Question 15 Random numbers generated by a __________ process
instead of a __________ process are pseudorandom numbers.
Question 16 __________ is a category of statistical techniques that
uses historical data to predict future behavior.
If the forecast for period 5 is equal to 275, use exponential smoothing
with α = .40 to compute a forecast for period 7.
Question 18 Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
Question 19 Consider the following demand and forecast.

Period Demand Forecast
1 7 10
2 12 15
3 18 20
4 22
If MAD = 2, what is the forecast for period 4?
Question 20 Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?

What is the expected value at node 4? Round your answer to the
nearest whole number. Do not include the dollar sign “$” in your
answer.
Question 31 A normal distribution has a mean of 500 and a standard
deviation of
the decimal.
Question 33 The following sales data are available for 2003-2008.
Determine a 4-year weighted moving average forecast for 2009, where
weights are W1 = 0.1, W2 = 0.2, W3 = 0.2 and W4 = 0.5.
Question 34 The following data summarizes the historical demand for
a product

Question 35 Robert wants to know if there is a relation between
money spent on gambling and winnings.
Question 36 Daily highs in Sacramento for the past week (from least
to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a
forecast for today using a 2 day moving average.
Question 37 Consider the following annual sales data for 2001-2008.
Calculate the correlation coefficient . Use four significant digits after
the decimal.

Question 38 Daily highs in Sacramento for the past week (from least
to most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a
forecast for today using a weighted moving average, with weights of .6,
.3 and .1, where the highest weights are applied to the most recent
data.
the decimal.
forecast.

Question 2 An inspector correctly identifies defective products 90%
of the time. For the next 10 products, the probability that he makes
fewer than 2 incorrect inspections is 0.736.
Question 5 Simulation results will always equal analytical results if
30 trials of the simulation have been conducted.
Question 6 A table of random numbers must be normally
distributed and efficiently generated.

Question 9 Assume that it takes a college student an average of 5
minutes to find a parking spot in the main parking l
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MAT 540 Week 1 Discussion Class Introductions
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"Class Introductions" Please respond to the following:
· Please introduce yourself, including your educational and career
goals, as well as some personal information about yourself. In your
introduction, please draw from your own experience (or use a search
engine) to give an example of how probability is used in your chosen
profession. If you get your information from an online or other
resource, be sure to cite the source of the information
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MAT 540 Week 1 Homework Chapter 1 and Chapter 11
(Solutions 100% Correct)
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MAT 540 Week 1 Homework Chapter 1
1. The Retread Tire Company recaps tires. The fixed annual cost of the
recapping operation is
$65,000. The variable cost of recapping a tire is $7.5. The company
charges$25 to recap a tire.
a. For an annual volume of 15, 000 tire, determine the total cost, total
revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire
Company operation.

2. Evergreen Fertilizer Company produces fertilizer. The company’s
fixed monthly cost is $25,000,
and its variable cost per pound of fertilizer is $0.20. Evergreen sells the
fertilizer for $0.45 per
pound. Determine the monthly break-even volume for the company.
3. If Evergreen Fertilizer Company in problem 2 changes the price of its
fertilizer from $0.45 per
pound to $0.55 per pound, what effect will the change have on the
break-even volume?
4. If Evergreen Fertilizer Company increases its advertising expenditure
by $10,000 per year, what
effect will the increase have on the break-even volume computed in
problem 2?
5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside
Tech’s football stadium

during home games. There are 6 home games scheduled for the
upcoming season. She must pay the
Tech athletic department a vendor’s fee of $3,000 for the season. Her
stand and other equipment
will cost her $3,500 for the season. She estimates that each hot dog she
sells will cost her $0.40. she
has talked to friends at other universities who sell hot dogs at games.
Based on their information
and the athletic department’s forecast that each game will sell out, she
anticipates that she will sell
approximately 1,500 hot dogs during each game.
a. What price should she charge for a hot dog in order to break even?
b. What factors might occur during the season that would alter the
volume sold and thus the
break-even price Annie might charge?
6. The college of business at Kerouac University is planning to begin an
online MBA program. The
initial start-up cost for computing equipment, facilities, course
development and staff recruitment
and development is $400,000. The college plans to charge tuition of
$20,000 per student per year.

However, the university administration will charge the college $10,000
per student for the first 100
students enrolled each year for administrative costs and its share of the
tuition payments.
a. How many students does the college need to enroll in the first year
to break-even?
b. If the college can enroll 80 students the first year, how much profit
will it make?
MAT540 Homework
c. The college believes it can increase tuition to $25,000, but doing so
would reduce enrollment to
50. Should the college consider doing this?
7. The following probabilities for grades in management science have
been determined based on past
records:
Grade Probability

A 0.1
B 0.2
C 0.4
D 0.2
F 0.10
1.00
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0,
and so on. Determine the
expected grade and variance for the course.
8. An investment firm is considering two alternative investments, A and
B, under two possible future
sets of economic conditions good and poor. There is a .60 probability of
good economic conditions
occurring and a .40 probability of poor economic conditions occurring.
The expected gains and
losses under each economic type of conditions are shown in the
following table:
Investment
Economic Conditions

Good Poor
A $380,000 -$100,000
B $130,000 $85,000
Using the expected value of each investment alternative, determine
which should be selected.
9. The weight of the bags of fertilizer is normally distributed, with a
mean of 45 pounds and a
standard deviation of 5 pounds. What is the probability that a bag of
fertilizer will weigh between
38 and 50 pounds
10. The polo Development Firm is building a shopping center. It has
informed renters that their rental
spaces will be ready for occupancy in 18 months. If the expected time
until the shopping center is
completed is estimated to be 15 months, with a standard deviation of 5
months, what is the
probability that the renters will not be able to occupy in 18 months?

11. The manager of the local National Video Store sells videocassette
recorders at discount prices. If
the store does not have a video recorder in stock when a customer
wants to buy one, it will lose the
sale because the customer will purchase a recorder from one of the
many local competitors. The
problem is that the cost of renting warehouse space to keep enough
recorders in inventory to meet
all demand is excessively high. The manager has determined that if 85%
of customer demand for
recorders can be met, then the combined cost of lost sales and
inventory will be minimized. The
manager has estimated that monthly demand for recorders is normally
distributed, with a mean of
175 recorders and a standard deviation of 55. Determine the number of
recorders the manager
should order each month to meet 85% of customer demand.
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MAT 540 Week 1-10 All Homework

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MAT 540 Week 1-11 All Discussion Question
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MAT 540 Week 2 Discussion Expected value of perfect information
MAT 540 Week 3 Discussion Simulation

MAT 540 Week 4 Discussion Forecasting Methods
MAT 540 Week 5 Discussion Reflection
MAT 540 Week 6 Discussion LP Models
MAT 540 Week 7 Discussion sensitivity analysis
MAT 540 Week 8 Discussion Practice setting up linear programming
models for business applications
MAT 540 Week 9 Discussion Application of Integer Programming
MAT 540 Week 10 Discussion Transshipment problems
MAT 540 Week 11 Discussion Reflection to Date
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MAT 540 Week 1-11 All Homework, DQs, Midterm (5
Set) , Final Exam (20 Set)

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MAT 540 Midterm Exam (5 Sets)
MAT 540 Final Exam (20 Sets)

MAT 540 Week 2 Discussion Expected value of perfect information

MAT 540 Week 8 Discussion Practice setting up linear programming
models for business applications
MAT 540 Week 9 Discussion Application of Integer Programming
MAT 540 Week 11 Discussion Reflection to Date
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MAT 540 Week 2 Discussion Expected value of perfect
information
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In your own words, explain how to obtain the “expected value of
perfect information” for any payoff table, which has probabilities
associated with each state of nature. Then, provide an example,
drawing from any of the payoff tables in Problems 1-17 in the back of
Chapter 12. If no probabilities are given for the states of nature, then
assume equal likelihood.
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MAT540
Week 2 Homework

Chapter 12
1. A local real estate investor in Orlando is considering three
alternative investments; a motel, a restaurant, or a theater. Profits
from the motel or restaurant will be affected by the availability of
gasoline and the number of tourists; profits from the theater will be
relatively stable under any conditions. The following payoff table shows
the profit or loss that could result from each investment:
Determine the best investment, using the following decision criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz (α = 0.4)
e. Equal likelihood

2. A concessions manager at the Tech versus A&M football game
must decide whether to have the vendors sell sun visors or umbrellas.
There is a 35% chance of rain, a 25% chance of overcast skies, and a
40% chance of sunshine, according to the weather forecast in college
junction, where the game is to be held. The manager estimates that the
following profits will result from each decision, given each set of
weather conditions:
a. Compute the expected value for each decision and select the
best one.
b. Develop the opportunity loss table and compute the expected
opportunity loss for each decision.
3. Place-Plus, a real estate development firm, is considering several
alternative development projects. These include building and leasing an
office park, purchasing a parcel of land and building an office building
to rent, buying and leasing a warehouse, building a strip mall, and
selling condominiums. The financial success of these projects depends
on interest rate movement in the next 5 years. The various
development projects and their 5- year financial return (in $1,000,000s)
given that interest rates will decline, remain stable, or increase, are in
the following payoff table. Place-Plus real estate development firm has
hired an economist to assign a probability to each direction interest

rates may take over the next 5 years. The economist has determined
that there is a
0.45 probability that interest rates will decline, a 0.35 probability that
rates will remain stable, and a
0.2 probability that rates will increase.
a. Using expected value, determine the best project.
b. Determine the expected value of perfect information.
4. The director of career advising at Orange Community College
wants to use decision analysis to provide information to help students
decide which 2-year degree program they should pursue. The director
has set up the following payoff table for six of the most popular and
successful degree programs at OCC that shows the estimated 5-Year
gross income ($) from each degree for four future economic conditions:

Determine the best degree program in terms of projected income,
using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz (α=0.4)
5. Construct a decision tree for the following decision situation and
indicate the best decision.
Fenton and Farrah Friendly, husband-and-wife car dealers, are soon
going to open a new dealership. They have three offers: from a foreign
compact car company, from a U.S. producer of full-sized cars, and from
a truck company. The success of each type of dealership will depend on
how much gasoline is going to be available during the next few years.
The profit from each type of dealership, given the availability of gas, is
shown in the following payoff table:
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Select one (1) of the following topics for your primary discussion
posting:
Identify the part of setting up a simulation in Excel that you find to be
the most challenging, and explain why.
Identify resources that can help you with that. Explain how simulation is
used in the real world.
Provide a specific example from your own line of work, or a line of work
that you find particularly interesting.

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1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3,
4, 5, or 6 hours, according to
the following probability distribution. The squad is on duty 24 hours per
day, 7 days per week:
Time Between
a. Simulate the emergency calls for 3 days (note that this will require a
“running” , or cumulative,
hourly clock), using the random number table.

b. Compute the average time between calls and compare this value
with the expected value of the
time between calls from the probability distribution. Why are the result
different?
2. The time between arrivals of cars at the Petroco Services Station is
defined by the following
probability distribution:
Time Between
a. Simulate the arrival of cars at the service station for 20 arrivals and
compute the average time
between arrivals.
b. Simulate the arrival of cars at the service station for 1 hour, using a
different stream of random
numbers from those used in (a) and compute the average time
between arrivals.
c. Compare the results obtained in (a) and (b).
3. The Dynaco Manufacturing Company produces a product in a process
consisting of operations of

five machines. The probability distribution of the number of machines
that will break down in a
week follows:
a. Simulate the machine breakdowns per week for 20 weeks.
b. Compute the average number of machines that will break down per
week.
4. Simulate the following decision situation for 20 weeks, and
recommend the best decision.
A concessions manager at the Tech versus A&M football game must
decide whether to have the
vendors sell sun visors or umbrellas. There is a 30% chance of rain, a
15% chance of overcast skies,
and a 55% chance of sunshine, according to the weather forecast in
college junction, where the
game is to be held. The manager estimates that the following profits
will result from each decision,
given each set of weather conditions:
MAT540 Homework

5. Every time a machine breaks down at the Dynaco Manufacturing
Company (Problem 3), either 1, 2,
or 3 hours are required to fix it, according to the following probability
distribution:
Repair Time (hr.) Probability
Simulate the repair time for 20 weeks and then compute the average
weekly repair time.
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Discuss Forecasting Methods

posting:
· Identify any challenges you have in setting up a time-series
analysis in Excel. Explain what they are and why they are challenging.
Identify resources that can help you with that.
· Explain how forecasting is used in the real world. Provide a
specific example from your own line of work, or a line of work that you
find particularly interesting.
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MAT 540 Homework Chapter 15
1. The manager of the Carpet City outlet needs to make an
accurate forecast of the demand for Soft Shag carpet (its biggest seller).

If the manager does not order enough carpet from the carpet mill,
customer will buy their carpet from one of Carpet City’s many
competitors. The manager has collected the following demand data for
the past 8 months: Compute a 3-month moving average forecast for
months 4 through 9.
a. Compute a weighted 3-month moving average forecast for
months 4 through 9. Assign weights of 0.55, 0.35, and 0.10 to the
months in sequence, starting with the most recent month.
b. Compare the two forecasts by using MAD. Which forecast
appears to be more accurate?
2. The manager of the Petroco Service Station wants to forecast
the demand for unleaded gasoline next month so that the proper
number of gallons can be ordered from the distributor. The owner has
accumulated the following data on demand for unleaded gasoline from
sales during the past 10 months:
a. Compute an exponential smoothed forecast, using an α value of
0.4

b. Compute the MAD.
3. Emily Andrews has invested in a science and technology mutual
fund. Now she is considering liquidating and investing in another fund.
She would like to forecast the price of the science and technology fund
for the next month before making a decision. She has collected the
following data on the average price of the fund during the past 20
months:
a. Using a 3-month average, forecast the fund price for month 21.
b. Using a 3-month weighted average with the most recent month
weighted 0.5, the next most recent month weighted 0.30, and the third
month weighted 0.20, forecast the fund price for month 21.
c. Compute an exponentially smoothed forecast, using α=0.3, and
forecast the fund price for month 21.
d. Compare the forecasts in (a), (b), and (c), using MAD, and
indicate the most accurate.
4. Carpet City wants to develop a means to forecast its carpet
sales. The store manager believes that the store’s sales are directly

related to the number of new housing starts in town. The manager has
gathered data from county records on monthly house construction
permits and from store records on monthly sales. These data are as
follows:
Monthly Carpet Sales Monthly Construction
(1,000 yd.) Permits
9 17
14 25
10 8
12 7
15 14
9 7
24 45
21 19
20 28

a. Develop a linear regression model for these data and forecast
carpet sales if 30 construction permits for new homes are filed.
b. Determine the strength of the causal relationship between
monthly sales and new home construction by using correlation.
5. The manager of Gilley’s Ice Cream Parlor needs an accurate
forecast of the demand for ice cream.
The store orders ice cream from a distributor a week ahead; if the store
orders too little, it loses business, and if it orders too much, the extra
must be thrown away. The manager belives that a major determinant
of ice cream sales is temperature (i.e.,the hotter the weather, the more
ice cream people buy). Using an almanac, the manager has determined
the average day time temperature for 14 weeks, selected at random,
and from store records he has determined the ice cream consumption
for the same 14 weeks. These data are summarized as follows:
a. Develop a linear regression model for these data and forecast
the ice cream consumption if the average weekly daytime temperature
is expected to be 85 degrees.

b. Determine the strength of the linear relationship between
temperature and ice cream consumption by using correlation.
c. What is the coefficient of determination? Explain its meaning.
==============================================
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Reflection to date• Please respond to the following: In a paragraph,
reflect on what you've learned so far in this course. Identify the most
interesting, unexpected, or useful thing you've learned and explain why
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Discuss LP Models
posting:
· The objective function always includes all of the decision
variables, but that is not necessarily true of the constraints. Explain the
difference between the objective function and the constraints. Then,
explain why a constraint need not refer to all the variables.
· Pick any constraint from any problem in the text, and explain how
to plot the line that corresponds to that constraint.
==============================================

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1. A Cereal Company makes a cereal from several ingredients. Two of
the ingredients, oats and rice,
provide vitamins A and B. The company wants to know how many
ounces of oats and rice it should
include in each box of cereal to meet the minimum requirements of 45
milligrams of vitamin A and
13 milligrams of vitamin B while minimizing cost. An ounce of oats
contributes 10 milligrams of
vitamin A and 2 milligram of vitamin B, whereas an ounce of rice
contributes 6 milligrams of A
and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of
rice costs $0.03.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

2. A Furniture Company produces chairs and tables from two resources-
labor and wood. The
company has 125 hours of labor and 45 board-ft. of wood available
each day. Demand for chairs is
limited to 5 per day. Each chair requires 7 hours of labor and 3.5 board-
ft. of wood, whereas a table
requires 14 hours of labor and 7 board-ft. of wood. The profit derived
from each chair is $325 and
from each table, $120. The company wants to determine the number of
chairs and tables to produce
each day in order to maximize profit. Formulate a linear programming
model for this problem.
b. Solve the model by using graphical analysis. (Do not round the
answers)
c. How much labor and wood will be unused if the optimal numbers of
chairs and tables are
produced?
3. Kroeger supermarket sells its own brand of canned peas as well as
several national brands. The

store makes a profit of $0.28 per can for its own peas and a profit of
$0.19 for any of the national
brands. The store has 6 square feet of shelf space available for canned
peas, and each can of peas
takes up 9 square inches of that space. Point-of-sale records show that
each week the store never
sales more than half as many cans of its own brand as it does of the
national brands. The store
wants to know how many cans of its own brand of peas of peas and
how many cans of the national
brands to stock each week on the allocated shelf space in order to
maximize profit.
b. Solve the model by using graphical analysis.
MAT540 Homework
4. Solve the following linear programming model graphically:
Minimize Z=8X1 + 6X2
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Discuss sensitivity analysis
posting:
· Identify any challenges you have in setting up a linear
programming problem in Excel, and solving it with Solver. Explain
exactly what the challenges are and why they are challenging. Identify
resources that can help you with that.
· Explain what the shadow price means in a maximization problem.
Explain what this tells us from a management perspective.
==============================================

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1. Southern Sporting Good Company makes basketballs and footballs.
Each product is produced from
two resources rubber and leather. Each basketball produced results in a
profit of $11 and each
football earns $15 in profit. The resource requirements for each
product and the total resources
available are as follows:
Product
Total resources available 600 900
a. Find the optimal solution.
b. What would be the effect on the optimal solution if the profit for the
basketball changed from

$11 to $12?
c. What would be the effect on optimal solution if 400 additional
pounds of rubber could be
obtained? What would be the effect if 600 additional square feet of
leather could be obtained?
2. A company produces two products, A and B, which have profits of $9
and $7, respectively. Each
unit of product must be processed on two assembly lines, where the
required production times are
as follows:
Product
Resource Requirements per Unit
Line 1 Line 2
A 11 5
B 6 9
Total Hours 65 40
a. Formulate a linear programming model to determine the optimal
product mix that will

maximize profit.
b. What are the sensitivity ranges for the objective function
coefficients?
c. Determine the shadow prices for additional hours of production time
on line 1 and line 2 and
indicate whether the company would prefer additional line 1 or line 2
hours.
3. Formulate and solve the model for the following problem:
Irwin Textile Mills produces two types of cotton cloth denim and
corduroy. Corduroy is a heavier
grade of cotton cloth and, as such, requires 8 pounds of raw cotton per
yard, whereas denim
requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4
hours of processing time;
a yard od denim requires 3.0 hours. Although the demand for denim is
practically unlimited, the
maximum demand for corduroy is 510 yards per month. The
manufacturer has 6,500 pounds of
cotton and 3,000 hours of processing time available each month. The
manufacturer makes a profit

of $2.5 per yards of denim and $3.25 per yard of corduroy. The
manufacturer wants to know how
many yards of each type of cloth to produce to maximize profit.
Formulate the model and put it
into standard form. Solve it
a. How much extra cotton and processing time are left over at the
optimal solution? Is the demand
for corduroy met?
b. If Irwin Mills can obtain additional cotton or processing time, but not
both, which should it
select? How much? Explain your answer.
4. The Bradley family owns 410 acres of farmland in North Carolina on
which they grow corn and
tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest;
each acre of tobacco costs
$210. The Bradleys’ have a budget of $52,500 for next year. The
government limits the number
of acres of tobacco that can be planted to 100. The profit from each
acre of corn is $300; the
profit from each acre of tobacco is $520. The Bradleys’ want to know
how many acres of each

crop to plant in order to maximize their profit.
a. Formulate the linear programming model for the problem and solve.
b. How many acres of farmland will not be cultivated at the optimal
solution? Do the Bradleys use
the entire 100-acre tobacco allotment?
c. The Bradleys’ have an opportunity to lease some extra land from a
neighbor. The neighbor is
offering the land to them for $110 per acre. Should the Bradleys’ lease
the land at that price?
What is the maximum price the Bradleys’ should pay their neighbor for
the land, and how
much land should they lease at that price?
MAT540 Homework
d. The Bradleys’ are considering taking out a loan to increase their
budget. For each dollar they
borrow, how much additional profit would they make? If they
borrowed an additional $1,000,
would the number of acres of corn and tobacco they plant change?

==============================================
MAT 540 Week 8 Assignment Linear Programming Case
Study You are a portfolio manager for the XYZ
investment fund
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Week 8 Project
You are a portfolio manager for the XYZ investment fund. The objective
for the fund is to maximize your portfolio returns from the investments
on four alternatives. The investments include (1) stocks, (2) real estate,
(3) bonds, and (4) certificate of deposit (CD). Your total investment
portfolio is $1,000,000.
Investment Returns

Based on the returns from the past five years, you concluded that the
investment annual returns on stocks are 10%, on real estates are 7% on
bonds are 4% and on CD is 1%.
Risk Constraints
However, you also have to analyze the risks associate with each
investment category. A wildly used risk measurement parameter is
called Value at Risk (VaR). (Note: VaR measures the risk of loss on a
specific portfolio of financial assets.) For example, given a million dollar
stock investment, if a portfolio of stocks has a one-day 4% VaR, there is
a 5% probability that the stock portfolio will fall in value by more than
1,000,000 * 0.004 = $4,000 over a one day period. In the portfolio, the
VaR for stock investments is 6%. Similarly, the VaR for real estate
investment is 2% and the VaR for bond investment is 1% and the VaR
for investment in CD is 0%. To manage the portfolio, you decided that
at 5% probability, your VaR for stocks cannot exceed $25,000, VaR for
real estate cannot exceed $15,000, VaR for bonds cannot exceed
$2,500 and the VaR for CD investment is $0.
Diversification and Liquidity Constraints

As a diversified investment portfolio, you also decided that each
investment category must hold at least $50,000 of the total investment
assets. In addition, you must hold combined CD and bond investment
no less than $200,000 in order to meet liquidity requirement.
The total amount of real estate holding shall not exceed 30% of the
portfolio assets.
A. As a portfolio manager, please formulate and solve the investment
portfolio problem using linear programming technique. What are the
amounts invest in (1) stocks, (2) real estate, (3) bonds and (4) CD?
B. If $500,000 additional investments are available to you in your
portfolio, how would you invest the capital?
C. Would you maintain the portfolio investment if stock yields lowered
to 6%? How would you re-distribute your investment portfolio?
==============================================
MAT 540 Week 8 Discussion Practice setting up linear
programming models for business applications

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MAT 540 WEEK 8 DISCUSSION
Practice setting up linear programming models for business
applications
Select an even-numbered LP problem from the text, excluding 14, 20,
22, 36 (which are part of your homework assignment). Formulate a
linear programming model for the problem you select.
==============================================
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Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for
Super Bowl Sunday, and she must determine how much beer to stock.
Betty stocks three brands of beer- Yodel, Shotz, and Rainwater. The
cost per gallon (to the tavern owner) of each brand is as follows:
Brand....................Cost/Gallon
Yodel.....................$1.50
Shotz...................... 0.90
Rainwater............... 0.50
The tavern has a budget of $2,000 for beer for Super Bowl Sunday.
Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon,
and Rainwater at $1.75 per gallon. Based on past football games, Betty
has determined the maximum customer demand to be 400 gallons of
Yodel, 500 gallons of shotz, and 300 gallons of Rainwater. The tavern
has the capacity to stock 1,000 gallons of beer; Betty wants to stock up
completely. Betty wants to determine the number of gallons of each
brand of beer to order so as to maximize profit.
b. Solve the model by using the computer.
2. As result of a recently passed bill, a congressman’s district has been
allocated $3 million for programs and projects. It is up to the

congressman to decide how to distribute the money. The congressman
has decide to allocate the money to four ongoing programs because of
their importance to his district- a job training program, a parks project,
a sanitation project, and a mobile library. However, the congressman
wants to distribute the money in a manner that will please the most
voters, or, in other words, gain him the most votes in the upcoming
election. His staff’s estimates of the number of votes gained per dollar
spent for the various programs are as follows.
Program....................Votes/Dollar
Job training................0.03
Parks.............................0.08
Sanitation....................0.05
Mobile library.............0.03
In order also to satisfy several local influential citizens who financed his
election, he is obligated to observe the following guidelines:
• None of the programs can receive more than 30% of the total
allocation
• The amount allocated to parks cannot exceed the total allocated to
both the sanitation project and the mobile library.
• The amount allocated to job training must at least equal the amount
spent on the sanitation project. Any money not spent in the district will
be returned to the government; therefore, the congressman wants to
spend it all. Thee congressman wants to know the amount to allocate
to each program to maximize his votes.

3. Anna Broderick is the dietician for the State University football team,
and she is attempting to determine a nutritious lunch menu for the
team. She has set the following nutritional guidelines for each lunch
serving:
• Between 1,300 and 2,100 calories
• At least 4 mg of iron
• At least 15 but no more than 55g of fat
• At least 30g of protein
• At least 60g of carbohydrates
• No more than 35 mg of cholesterol
She selects the menu from seven basic food items, as follows, with the
nutritional contributions per pound and the cost as given:
............ Calories......Iron....Protein
...Carbohydrates....Fat....Cholesterol......Cost
............. (Per
lb).......(mg/lb).....(g/lb)........(g/lb)..............(g/lb).........(mg/lb)..........($/lb
)
Chicken 500 4.2 17 0 30 180 0.85
Fish 480 3.1 85 0 5 90 3.35

Ground beef 840 0.25 82 0 75 350 2.45
Dried beans 590 3.2 10 30 3 0 0.85
Lettuce 40 0.4 6 0 0 0 0.70
Potatoes 450 2.25 10 70 0 0 0.45
Milk (2%) 220 0.2 16 22 10 20 0.82
The dietician wants to select a menu to meet the nutritional guidelines
while minimizing the total cost per serving.
a. Formulate a linear programming model for this problem and solve.
b. If a serving of each of the food items (other than milk) was limited to
no more than a half pound, what effect would this have on the
solution?
4. Dr. Maureen Becker, the head administrator at Jefferson County
Regional Hospital, must determine a schedule for nurses to make sure
there are enough of them on duty throughout the day. During the day,
the demand for nurses varies. Maureen has broken the day in to twelve
2- hour periods. The slowest time of the day encompasses the three
periods from 12:00 A.M. to 6:00 A.M., which beginning at midnight;
require a minimum of 30, 20, and 40 nurses, respectively. The demand
for nurses steadily increases during the next four daytime periods.
Beginning with the 6:00 A.M.- 8:00 A.M. period, a minimum of 50, 60,
80, and 80 nurses are required for these four periods, respectively.
After 2:00 P.M. the demand for nurses decreases during the afternoon
and evening hours. For the five 2-hour periods beginning at 2:00 P.M.

and ending midnight, 70, 70, 60, 50, and 50 nurses are required,
respectively. A nurse reports for duty at the beginning of one of the 2-
hour periods and works 8 consecutive hours (which is required in the
nurses’ contract). Dr. Becker wants to determine a nursing schedule
that will meet the hospital’s minimum requirement throughout the day
while using the minimum number of nurses.
5. The production manager of Videotechnics Company is attempting to
determine the upcoming 5-month production schedule for video
recorders. Past production records indicate that 2,000 recorders can be
produced per month. An additional 600 recorders can be produced
monthly on an overtime basis. Unit cost is $10 for recorders produced
during regular working hours and $15 for those produced on an
overtime basis. Contracted sales per month are as follows: Month
Contracted Sales (units) 1 1200 2 2100 3 4 5 2400 3000 4000 Inventory
carrying costs are $2 per recorder per month. The manager does not
want any inventory carried over past the fifth month. The manager
wants to know the monthly production that will minimize total
production and inventory costs. a. Formulate a linear programming
model for this problem. b. Solve the model by using the computer.
==============================================

MAT 540 Week 9 Discussion Application of Integer
Programming
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Week 9 Discussion
Explain how the applications of Integer programming differ from those
of linear programming. Give specific instances in which you would use
an integer programming model rather than an LP model. Provide real-
world examples.
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MAT 540 Week 9 Homework - Chapter 5
1. Rowntown Cab Company has 70 drivers that it must schedule in
three 8-hour shifts. However, the demand for cabs in the metropolitan
area varies dramatically according to time of the day. The slowest
period is between midnight and 4:00 A.M. the dispatcher receives few
calls, and the calls that are received have the smallest fares of the day.
Very few people are going to the airport at that time of the night or
taking other long distance trips. It is estimated that a driver will average
$80 in fares during that period. The largest fares result from the airport
runs in the morning. Thus, the drivers who sart their shift during the
period from 4:00 A.M. to 8:00 A.M. average $500 in total fares, and
drivers who start at 8:00 A.M. average $420. Drivers who start at noon
average $300, and drivers who start at 4:00 P.M. average $270. Drivers
who start at the beginning of the 8:00 P.M. to midnight period earn an
average of $210 in fares during their 8-hour shift.
To retain customers and acquire new ones, Rowntown must maintain a
high customer service level. To do so, it has determined the minimum
number of drivers it needs working during every 4-hour time segment-
10 from midnight to 4:00 A.M. 12 from 4:00 to 8:00 A.M. 20 from 8:00
A.M. to noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M.,
and 18 from 8:00 P.M. to midnight.
a. Formulate and solve an integer programming model to help
Rowntown Cab schedule its drivers.

b. If Rowntown has a maximum of only 15 drivers who will work the
late shift from midnight to 8:00 A.M., reformulate the model to reflect
this complication and solve it
c. All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M.,
so the company has decided to limit the number of drivers who work
this 8-hour shift to 20. Reformulate the model in (b) to reflect this
restriction and solve it.
2.
2. Juan Hernandez, a Cuban athlete who visits the United States and
Europe frequently, is allowed to return with a limited number of
consumer items not generally available in Cuba. The items, which are
carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan
is in Cuba, he sells the items at highly inflated prices. The weight and
profit (in U.S. dollars) of each item are as follows: Item Weight (lb.)
Profit Denim jeans 2 $90 CD players 3 150 Compact discs 1 30 Juan
wants to determine the combination of items he should pack in his
duffel bag to maximize his profit. This problem is an example of a type
of integer programming problem known as a
“knapsack” problem. Formulate and solve the problem.
3. The Texas Consolidated Electronics Company is contemplating a
research and development program encompassing eight research
projects. The company is constrained from embarking on all projects by

the number of available management scientists (40) and the budget
available for R&D projects ($300,000). Further, if project 2 is selected,
project 5 must also be selected (but not vice versa). Following are the
resources requirement and the estimated profit for each project.
Project Expense Management Estimated Profit ($1,000s) Scientists
required (1,000,000s) 1 50 6 0.30 2 105 8 0.85 3 56 9 0.20 4 45 3 0.15 5
90 7 0.50 6 80 5 0.45 7 78 8 0.55 8 60 5 0.40 Formulate the integer
programming model for this problem and solve it using the computer.
Corsouth Mortgage Associates is a large home mortgage firm in the
southeast. It has a poll of permanent and temporary computer
operators who process mortgage accounts, including posting payments
and updating escrow accounts for insurance and taxes. A permanent
operator can process 220 accounts per day, and a temporary operator
can process 140 accounts per day. On average, the firm must process
and update at least 6,300 accounts daily. The company has 32
computer workstations available. Permanent and temporary operators
work 8 hours per day. A permanent operator averages about 0.4 error
per day, whereas a temporary operator averages 0.9 error per day. The
company wants to limit errors to 15 per day. A permanent operator is
paid $120 per day wheras a temporary operator is paid $75 per day.
Corsouth wants to determine the number of permanent and temporary
operators it needs to minimize cost. Formulate, and solve an integer
programming model for this problem and compare this solution to the
non-integer solution.

5. Globex Investment Capital Corporation owns six companies that have
the following estimated returns (in millions of dollars) if sold in one of
the next 3 years:
Year Sold (estimated returns, $1,000,000s) Company 1 2 3 1 $14 $18
$232 9 11 153 18 23 274 16 21 255 12 16 226 21 23 28 To generate
operating funds, the company must sell at least $20 million worth of
assets in year 1, $25 million in year 2, and $35 million in year 3. Globex
wants to develop a plan for selling these companies during the next 3
years to maximize return.
Formulate an integer programming model for this problem and solve it
by using the computer.
==============================================
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Discussion assignment and transshipment problems

posting:
· Explain the assignment model and how it facilitates in solving
transportation problems. Determine the benefits to be gained from
using this model.
· Identify any challenges you have in setting up an transshipment
model in Excel, and solving it with Solver. Explain exactly what the
challenges are and why they are challenging. Identify resources that can
help you with that.
==============================================
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1. Consider the following transportation problem:

From To (Cost) Supply 1 2 3 A 6 5 5 150 B 11 8 9 85 C 4 10 7 125
Demand 70 100 80
Formulate this problem as a linear programming model and solve it by
the using the computer.
2. Consider the following transportation problem:
From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150
Demand 110 140 100 Solve it by using the computer.
3. World foods, Inc. imports food products such as meats, cheeses, and
pastries to the United States from warehouses at ports in Hamburg,
Marseilles and Liverpool. Ships from these ports deliver the products to
Norfolk, New York and Savannah, where they are stored in company
warehouses before being shipped to distribution centers in Dallas, St.
Louis and Chicago. The products are then distributed to specialty foods
stores and sold through catalogs. The shipping costs ($/1,000 lb.) from
the European ports to the U.S. cities and the available supplies (1000
lb.) at the European ports are provided in the following table: From To
(Cost) Supply 4. Norfolk 5. New York 6. Savannah 1. Hamburg 320 280
555 75 2. Marseilles 410 470 365 85 3. Liverpool 550 355 525 40

The transportation costs ($/1000 lb.) from each U.S. city of the three
distribution centers and the demands (1000 lb.) at the distribution
centers are as follows:
Warehouse Distribution Center 7. Dallas 8. St. Louis 9. Chicago 4.
Norfolk 80 78 85 5. New York 100 120 95 6. Savannah 65 75 90 Demand
85 70 65 Determine the optimal shipments between the European
ports and the warehouses and the distribution centers to minimize
total transportation costs.
4. The Omega Pharmaceutical firm has five salespersons, whom the
firm wants to assign to five sales regions. Given their various previous
contacts, the sales persons are able to cover the regions in different
amounts of time. The amount of time (days) required by each
salesperson to cover each city is shown in the following table:
Salesperson Region (days) A B C D E 1 20 10 12 10 22 2 14 10 18 11 15 3
12 13 19 11 14 4 16 12 14 22 16 5 12 15 19 26 23 Which salesperson
should be assigned to each region to minimize total time? Identify the
optimal assignments and compute total minimum time.
==============================================

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