# MAT 540 – In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected University, Washington DC MAT 540 Final Exam 2014

• Question 1

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ? 0 implies that if project 2 is selected, project 1 cannot be selected.

• Question 2

• Question 3

A cycle is an up and down movement in demand that repeats itself in less than 1 year.

• Question 4

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

• Question 5

In a transshipment problem, items may be transported from destination to destination and from source to source.

• Question 6

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.

• Question 7

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The conservative (maximin) strategy is:

• Question 8

Events that cannot occur at the same time in any trial of an experiment are:

• Question 9

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:

• Question 10

In linear programming problems, multiple optimal solutions occur

• Question 11

In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?

• Question 12

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$100 and requires 100 cubic feet of storage space, and each medium shelf costs \$50 and requires 80 cubic feet of storage space. The company has \$25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$85 and for each medium shelf is \$75. What is the objective function?

• Question 13

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$100 and requires 100 cubic feet of storage space, and each medium shelf costs \$50 and requires 80 cubic feet of storage space. The company has \$25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$85 and for each medium shelf is \$75. What is the storage space constraint?

• Question 14

The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are \$2 per bottle, and profits for dark beer are \$1 per bottle. What is the optimal weekly profit?

• Question 15

The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:

The Sensitivity Report:

Which additional resources would you recommend to be increased?

• Question 16

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds)

1 20 24 30

2 30 10 50

3 0 30 20

4 24 15 60

5 10 20 40

The constraint for ingredient 3 is:

• Question 17

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to \$50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?

• Question 18

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

• Question 19

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

• Question 20

A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.

Which of the following constraints represents the assignment for student A?

• Question 21

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.

The constraint that represents the quantity supplied by DC 1 is:

• Question 22

Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other. This means that they are:

• Question 23

The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Note: please provide your answer to 2 places past the decimal point, rounding as appropriate.

• Question 24

__________ moving averages react more slowly to recent demand changes than do __________ moving averages.

• Question 25

A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed.

Number of Arrivals Probability Random numbers

6 .1 .01 – .10

7 .3 .11 – .40

8 .3 .41 – .70

9 .2 .71 – .90

10 .1 .91 – .00

Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?

• Question 26

Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?

• Question 27

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

• Question 28

Carter’s Bed & Breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is \$1050 per month and the revenue they receive from each booked room is \$150. What is the variable cost per occupied room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write \$105.00).

• Question 29

Ford’s Bed & Breakfast breaks even if they sell 50 rooms each month. They have a fixed cost of \$6500 per month. The variable cost per room is \$30. For this model to work, what must be the revenue per room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write \$105.00).

• Question 30

Students are organizing a “Battle of the Bands” contest. They know that at least 100 people will attend. The rental fee for the hall is \$200 and the winning band will receive \$500. In order to guarantee that they break even, how much should they charge for each ticket? (Note: Write your answer with two significant places after the decimal and do not include the dollar “\$” sign. For instance, for five dollars, write your answer as 5.00).

• Question 31

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of \$30 on each tractor and \$30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation:

Let x = number of tractors produced per period

y = number of lawn mowers produced per period

MAX 30x + 30y

subject to 2 x + y ? 60

2 x + 3y ? 120

x ? 45

x, y ? 0

The graphical solution is shown below.

What is the shadow price for fabrication? Write your answers with two significant places after the decimal and do not include the dollar “\$” sign.

• Question 32

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of \$30 on each tractor and \$30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation:

Let x = number of tractors produced per period

y = number of lawn mowers produced per period

MAX 30x + 30y

subject to 2 x + y ? 60

2 x + 3y ? 120

x ? 45

x, y ? 0

The graphical solution is shown below.

What is the shadow price for assembly? Write your answers with two significant places after the decimal and do not include the dollar “\$” sign.

• Question 33

Kalamazoo Kennels provides overnight lodging 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:

Cat Food Cost/oz protien (%) fat (%)

Pet’s Choice 0.35 40 15

Feline Chow 0.32 20 30

Kalamazoo 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 optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “\$” sign. For instance, \$9.45 (nine dollars and fortyfive cents) should be written as 9.45

• Question 34

Find the optimal Z value for the following problem. Do not include the dollar “\$” sign with your answer.

MAX Z = 5×1 + 8×2

s.t. x1 + x2 ? 6

5×1 + 9×2 ? 45

x1, x2 ? 0 and integer

• Question 35

A life insurance company wants to update its actuarial tables. 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 participants are expected to survive to see their 75th birthday? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.

• Question 36

Ms. Hegel is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

Investment Economic Conditions

Poor

(S1) Average

(S2) Good

(S3) Excellent

(S4)

A 80 15 18 47

B 50 75 35 35

C -90 225 -50 12

D 36 25 25 27

Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable

• Question 37

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 probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = \$50,000). 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 38

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 probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “\$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = \$50,000). 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 39

Recent past demand for product DEF is given in the following table.

Month Actual Demand

May 19

June 20

July 23

August 21

The forecasted demand for May, June, July and August were 17, 18, 20 and 24 respectively. Determine the value of MAD. Note: Please express the result as a number with 2 decimal places. If necessary, round your result accordingly. For instance, 9.146, should be expressed as 9.15

• Question 40

Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “\$” sign with your answer.

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