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MAT 540 Final Exam Latest

MAT540

MAT 540 Final Exam Latest

Question 1

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

variables.

Question 2

In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ?

signs.

Question 3

Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

Question 4

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

Question 5

In a total integer model, all decision variables have integer solution values.

Question 6

Validation of a simulation model occurs when the true steady state average results have been reached.

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

Using the minimax regret criterion to make a decision, you

Question 10

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 11

Using the maximin criterion to make a decision, you

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.In order to maximize profit, how many big shelves (B) and how many medium

shelves (M) should be purchased?

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 constraint on money to invest?

Question 14

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4

lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the

amount of this resource by 1 lb. will result in the:

Question 15

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

The Answer Report:

The Sensitivity Report:

Which additional resources would you recommend to be increased?

Question 16

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. An appropriate part of the model would be

Question 17

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.

Minimum daily requirement

(pounds)

30

50

20

60

40

Ingredient

Percent per pound in Feed A

Percent per pound in Feed B

1

2

3

4

5

20

30

0

24

10

24

10

30

15

20

The constraint for ingredient 3 is:

Question 18

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

Question 19

The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different

machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used,

machine 1 will not be used.

Question 20

The assignment problem constraint x31+x32+x33+x34 ? 2 means

Question 21

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 22

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. What

percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking

lot?

Question 23

Professor Truman would like to assign grades such that 10% of students receive As. If the exam average

is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

Question 24

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

6

7

8

9

10

Probability

.1

.3

.3

.2

.1

Random numbers

.01 – .10

.11 – .40

.41 – .70

.71 – .90

.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 25

For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a

demand of:

Question 26

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Question 27

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

averages.

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

Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX

s.t.

1.2R + 1.6 S ? 600 assembly (hours)

0.8R + 0.5 S ? 300 paint (hours)

.16R + 0.4 S ? 100 inspection (hours)

Sensitivity Report:

Cell

$B$7

$C$7

Cell

$E$3

$E$4

$E$5

Final

Value

291.67

133.33

Final

Value

Reduced

Cost

0.00

0.00

Shadow

Price

0.00

33.33

145.83

Objective

Coefficient

50

75

Constraint

R.H. Side

600

300

100

Allowable

Increase

70

50

Allowable

Increase

1E+30

39.29

12.94

Allowable

Decrease

20

43.75

Allowable

Decrease

36.67

175

40

Name

Regular =

Super =

Name

Assembly (hr/unit) 563.33

Paint (hr/unit)

Inspect (hr/unit)

300.00

100.00

If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would

be reduced by __________. 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

Klein 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

Partner’s Choice

Feline Excel

Cost/oz

$0.20

$0.15

protien (%)

45

15

fat (%)

20

30

Klein 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 forty-

five 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

Let’s say that 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 72

years and a standard deviation of 5 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. James 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.

Poor (S1)

A

B

C

D

Economic Conditions

Average (S2)

18

19

100

20

Good (S3)

25

100

26

27

Excellent (S4)

50

50

120

50

80

75

60

240

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 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 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 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 39

The following sales data are available for 2003-2008 :

Year

2003

2004

2005

2006

2007

2008

Sales

7

12

14

20

16

25

Forecast

9

10

15

22

18

21

Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4

decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed

as 9.1468

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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