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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)
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
Question 15 Pseudorandom numbers exhibit __________ in order to
be considered truly random.
Question 16 __________ is a category of statistical techniques that
uses historical data to predict future behavior.
Question 17 __________ methods are the most common type of
forecasting method for the long-term strategic planning process.
Question 18 __________ is a linear regression model relating
demand to time.
Question 19 rob 14, and 15)estion 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 In exponential smoothing, the closer alpha is to
__________,the greater the reaction to the most recent demand.
Question 21 __________ is absolute error as a percentage of
demand.
Question 22 Consider the following graph of sales. Which of the
following characteristics is exhibited by the data?
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 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:

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MAT 540 Week 1 Discussion Class
Introductions
"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)

MAT 540 Week 1 Homework Chapter 1
1. The Retread Tire Company
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
MAT 540 Week 1 Homework Chapter 1 and Chapter 11
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MAT 540 Week 1-11 All Discussion Question
MAT 540 Week 1 Discussion Class Introductions
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)
MAT 540 Midterm Exam (5 Sets)
MAT 540 Final Exam (20 Sets)
MAT 540 Week 1 Homework Chapter 1 and Chapter 11
MAT 540 Week 1 Discussion Class Introductions

MAT 540 Week 2 Discussion Expected value of perfect information
MAT 540 Week 4 Discussion Forecasting Methods
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 2 Discussion Expectedvalue of
perfect information

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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MAT 540 Week 2 Quiz 1 (3 Sets)
MAT 540 Week 2 Quiz 1 Set 1 QUESTIONS
Question 1: Parameters are known, constant values that are usually
coefficients of variables in equations.
Question 2: If variable costs increase, but price and fixed costs are
held constant, the break even point will decrease.
Question 3: Probabilistic techniques assume that no uncertainty
exists in model parameters.
Question 4: Fixed cost is the difference between total cost and total
variable cost.
Question 5: A binomial probability distribution indicates the
probability of r successes in n trials.
Question 6: The events in an experiment are mutually exclusive if
only one can occur at a time.

Question 7: If events A and B are independent, then P(A|B) =
P(B|A).
Question 8: If fixed costs increase, but variable cost and price remain
the same, the break even point
Question 9: If the price
that 20 people will attend, what price should be charged per person to
process requires a fixed cost of $50,000. The variable cost per unit is
$25 and the revenue per unit is projected to be $45. Find the break-
even point.
Question 18 Wei is considering pursuing an MS in Information
Systems degree. She has applied to two different universities. The
acceptance rate for applicants with similar qualifications is 20% for
University X and 45% for University Y. What is the probability that
Wei will be accepted by at least one of the two universities? {Express
your answer as a percent. Round (if necessary) to the nearest whole
percent and omit the decimal. For instance, 20.1% would be written
as 20}
Question 19 The variance of the standard normal distribution is equal
to __________.
Question 20 An automotive center keeps tracks of customer
complaints received each week. The probability distribution for
complaints can be represented as a table (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? Note:
Please report your answer with two places to the right of the decimal,
rounding if appropriate.
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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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MAT 540 Week 3 Quiz 2 (Two Sets)

Question 1 If two events are not mutually exclusive, then P(A or B) =
P(A) + P(B)
Question 2 Probability trees are used only to compute conditional
probabilities.
Question 3 Seventy two percent of all observations fall within 1
standard deviation of the mean if the data is normally distributed.
Question 4 Both maximin and minimin criteria are optimistic.
Question 5 The equal likelihood criterion assigns a probability of 0.5
to each state of nature, regardless of how many states of nature there
are.
Question 6 The Hurwicz criterion is a compromise between the
minimax and minimin criteria.
Question 7 Using the minimax regret criterion, we first construct a
table of regrets. Subsequently, for each possible decision, we look
across the states of nature and make a note of the maximum regret
possible for that decision. We then pick the decision with the largest
maximum regret.
Question 8 Assume that it takes a college student an average of 5
minutes to find a parking spot in the main parking lot. Assume also
that this time is normally distributed with a standard deviation of 2
minutes. Find the probability that a randomly selected college student
will take between 2
Alt S1 S2
1 10 2
2 -2 8
3 8 5

Compute the expected value of perfect information assuming that the
probability of S2 is equal to 0.4.
Question 19 A group of friends are planning a recreational outing and
have constructed the following payoff table to help them decide
which activity to engage in. Assume that the payoffs represent their
level of enjoyment for each activity under the various weather
conditions.
Weather
Cold Warm Rainy
S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
Question 20 If the probabilities of cold weather (S1), warm weather
(S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is
the EVPI for this situation?
Consider the following decision tree.
What is the expected value for the best decision? Round your answer
to the nearest whole number.
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MAT 540 Week 4 Discussion Forecasting
Methods

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. 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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MAT 540 Week 7 Discussion sensitivity
analysis
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
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?
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MAT 540 Week 7 Quiz 3 (Three Sets)
Question 1: Graphical solutions to linear programming problems have
an infinite number of possible objective function lines.
Question 2: The following inequality represents a resource constraint
for a maximization problem:
X + Y ≥ 20
Question 3: In minimization LP problems the feasible region is
always below the
represents the feasible region, and the dashed line in the middle is the
slope of the objective function. What would be the new slope of the
objective function if multiple optimal solutions occurred along line
segment AB? Write your answer in decimal notation.
Question 19: Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to: 8x + 5y ≤ 40

0.4x + y ≥ 4
x, y ≥ 0
At the optimal solution, what is the amount of slack associated with
the first constraint?
Question 20: Consider the following minimization problem:
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
Find the optimal solution. What is the value of the objective function
at the optimal solution? Note: The answer will be an integer. Please
give your answer as an integer without any decimal point. For
example, 25.0 (twenty five) would be written 25
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MAT 540 Week 8 Assignment Linear
Programming Case Study You are a portfolio
manager for the XYZ investment fund
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?
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MAT 540 Week 8 Discussion Practice setting
up linear programming models for business
applications
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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1. 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

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.
b. Solve the model by using the computer.
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.
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MAT 540 Week 9 Discussion Application of
Integer Programming
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
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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MAT 540 Week 9 Quiz 4 Set (Three Sets)

Question 1: When using a linear programming model to solve the
"diet" problem, the objective is generally to maximize profit.
Question 2: In a balanced transportation model, supply equals demand
such that all constraints can be treated as equalities.
Question 3: In a transportation problem, a demand constraint (the
amount of product demanded at a given destination) is a less-than-or
equal-to constraint (≤).
Question 4: Fractional relationships between variables are permitted
in the standard form of a linear program.
Question 5: The standard form for the computer solution of a linear
programming problem requires all variables to be to the right and all
numerical values to be to the left of the inequality or equality sign
Question 6: A systematic approach to model formulation is to first
construct the objective function before determining the decision
variables.
Question 7: A croissant shop produces 2 products: bear claws (B) and
almond filled croissants (C). Each bear claw requires 6 ounces of
flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled
croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of
almond paste. The company has 6600 ounces of flour, 1400 ounces of
yeast, and 4800 TS of almond
for a variety of pets. An attractive feature is the quality of care the
pets receive, including well balanced nutrition. The kennel's cat food
is made by mixing two types of cat food to obtain the "nutritionally
balanced cat diet." The data for the two cat foods are as follows:
Kitty Kennels wants to be sure that the cats receive at least 5 ounces
of protein and at least 3 ounces of fat per day. What is the cost of this
plan? Express your answer with two places to the right of the decimal
point. For instance, $9.32 (nine dollars and thirty-two cents) would be
written as 9.32
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MAT 540 Week 10 Discussion Transshipment
problems
Discussion assignment and transshipment problems
posting:
• Explain the assignment model and how it facilitates in solving
transportation problems. Determine the benefits to be gained from
using this model.
• Identify any challenges you have in setting up an transshipment
model in Excel, and solving it with Solver. Explain exactly what the
challenges are and why they are challenging. Identify resources that
can help you with that.
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1. Consider the following transportation problem:
From To (Cost) Supply 1 2 3 A 6 5 5 150 B 11 8 9 85 C 4 10 7 125
Demand 70 100 80
Formulate this problem as a linear programming model and solve it
by the using the computer.
2. Consider the following transportation problem:
From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150
Demand 110 140 100 Solve it by using the computer.
3. World foods, Inc. imports food products such as meats, cheeses,
and pastries to the United States from warehouses at ports in
Hamburg, Marseilles and Liverpool. Ships from these ports deliver
the products to Norfolk, New York and Savannah, where they are
stored in company warehouses before being shipped to distribution
centers in Dallas, St. Louis and Chicago. The products are then
distributed to specialty foods stores and sold through catalogs. The
shipping costs ($/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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MAT 540 Week 10 Quiz 5 (Three Sets)
Question 1: Rounding non-integer solution values up to the nearest
integer value will result in an infeasible solution to an integer linear
programming problem.
Question 2: The solution to the LP relaxation of a maximization
integer linear program provides an upper bound for the value of the
objective function.
Question 3: If we are solving a 0-1 integer programming problem
with three decision variables, the constraint x1 + x2 ≤ 1 is a mutually
exclusive constraint.

Question 4: A conditional constraint specifies the conditions under
which variables are integers or real variables.
Question 5: If we are solving a 0-1 integer programming problem
with three decision variables, the constraint x1 + x2 + x3 ≤ 3 is a
mutually exclusive constraint.
Question 6: If exactly 3 projects are to be selected from a set of 5
projects, this would be written as 3 separate constraints in an integer
program.
Question 7: The Wiethoff Company has a contract to produce 10000
garden hoses for a customer. Wiethoff has 4 different machines that
can produce this kind of hose. Because these machines are from
different manufacturers and use differing technologies, their
specifications are not the same.
Write the constraint that indicates they can purchase no more than 3
machines.
Question 8: In a 0-1 integer programming model, if the constraint x1-
x2 = 0, it means when project 1 is selected, project 2 __________ be
selected.
Question 9: Assume that we are using 0-1 integer programming
model to solve a capital budgeting problem and xj = 1 if project j is
selected and xj = 0, otherwise.
The constraint (x1 + x2 + x3 + x4 ≤ 2) means that __________ out of
the 4 projects must be selected.
Question 10: If we are solving a 0-1 integer programming problem,
the constraint x1 + x2 ≤ 1 is a __________ constraint.
the constraint x1 = x2 is a __________ constraint.
Question 12: If the solution values of a linear program are rounded in
order to obtain an integer solution, the solution is
the constraint x1 + x2 = 1 is a __________ constraint.

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