**Question 1**

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

Answer

True

False

**Question 2**

If we are solving a 0-1 integer programming problem, the constraint *x*1 = *x*2 is a conditional constraint.

Answer

True

False

**Question 3**

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

Answer

True

False

**Question 4**

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

Answer

True

False

**Question 5**

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.

Answer

True

False

**Question 6**

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

Answer

True

False

**Question 7**

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

Answer

exhaustive

dependent

independent

mutually exclusive

**Question 8**

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:

Answer

Buy

Rent

Lease

Brisk.

**Question 9**

Using the maximin criterion to make a decision, you

Answer

Construct a table of regrets. Look at the maximum regret for each decision. Select the decision with the smallest maximum regret.

Look at the worst payoff for each possible decision and select the decision with the largest worst payoff

Look at the best payoff for each possible decision and select the decision with the largest best payoff

Consult an astrological table to forecast the state of nature

**Question 10**

An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.

Answer

a decision variable.

a parameter.

an objective function.

a constraint.

**Question 11**

The probability of observing *x*

successes in a fixed number of trials is a problem related to

Answer

the normal distribution

the binomial distribution

conditional probability

the Poisson distribution

**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 storage space constraint?

Answer

Max + 85M

100B + 50M ≥ 25000

100B + 80M ≤ 18000

100B + 80M = 18000

**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. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

Answer

,

,

,

,

**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:

Answer

same product mix, different total profit

different product mix, same total profit as before

same product mix, same total profit

different product mix, different total profit

**Question 15**

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?

Answer

$1000

$900

$800

$700

**Question 16**

Compared to transportation LP problems, assignment problems are unique because

Answer

The supply at each source is limited to 1 unit.

The demand at each destination is limited to 1 unit.

Both of the above

None of the above.

**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?

Answer

X1 ≤ 0.35

X1 = 0.35 (50000)

X1 ≤ 0.35(X1 + X2 + X3)

(X1 + X2 + X3)

**Question 18**

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.

Answer

Y1 + Y4 ≤ 0

Y1 + Y4 = 0

Y1 + Y4 ≤ 1

Y1 + Y4 ≥ 1

**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 the constraint that indicates they have to use at least three of the five machines in their production.

Answer

Y1 + Y2 + Y3 + Y4

+ Y5 ≤ 3

Y1 + Y2 + Y3 + Y4

+ Y5 = 3

Y1 + Y2 + Y3 + Y4

+ Y5 ≥ 3

none of the above

**Question 20**

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

Answer

agent 3 can be assigned to 2 tasks

agent 3 can be assigned to no more than 2 tasks

a mixture of agents 1, 2, 3 and 4 will be assigned to tasks

agent 2 can be assigned to 3 tasks

**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 demanded by Customer B is:

Answer

6X1B + 2X2B + 8X3B ≤ 350

6X1B + 2X2B + 8X3B = 350

X1B + X2B + X3B ≤ 350

X1B + X2B + X3B = 350

**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:

Answer

mutually exclusive

independent

controlled by the central limit theorem

all of the above

**Question 23**

Professor Dewey would like to assign grades such that 15% 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.)

Answer

75

79

84

88

**Question 24**

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Answer

Trend only

Trend plus seasonal

Trend plus irregular

Seasonal

**Question 25**

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?

Answer

36.9

57.5

60.5

62.5

**Question 26**

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?

Answer

23

24

22

25

**Question 27**

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

Answer

Longer-period, shorter-period

Shorter-period, longer-period

Longer-period, longer-period

Shorter-period, shorter-period

**Question 28**

Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200. The variable cost per room is $75. How many rooms do they have to sell each month to break even? *(Note: The answer is a whole number. Give the answer as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms). *

Answer

**Question 29**

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). *

Answer

**Question 30**

Joseph 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. What is the probability that Jim will not be accepted at either university? *(Note: write your answer as a probability, with two decimal places. If necessary, round to two decimal places. For instance, a probability of 0.252 should be written as 0.25). *

Answer

**Question 31**

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

MAX

50R + 75S

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:**

**Final**

**Reduced**

**Objective**

**Allowable**

**Allowable**

**Cell**

**Name**

**Value**

**Cost**

**Coefficient**

**Increase**

**Decrease**

$B$7

Regular =

291.67

0.00

50

70

20

$C$7

Super =

133.33

0.00

75

50

43.75

**Final**

**Shadow**

**Constraint**

**Allowable**

**Allowable**

**Cell**

**Name**

**Value**

**Price**

**R.H. Side**

**Increase**

**Decrease**

$E$3

Assembly (hr/unit)

563.33

0.00

600

1E+30

36.67

$E$4

Paint (hr/unit)

300.00

33.33

300

39.29

175

$E$5

Inspect (hr/unit)

100.00

145.83

100

12.94

40

A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

Answer

5 points

**Question 32**

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

MAX

50R + 75S

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:**

**Final**

**Reduced**

**Objective**

**Allowable**

**Allowable**

**Cell**

**Name**

**Value**

**Cost**

**Coefficient**

**Increase**

**Decrease**

$B$7

Regular =

291.67

0.00

50

70

20

$C$7

Super =

133.33

0.00

75

50

43.75

**Final**

**Shadow**

**Constraint**

**Allowable**

**Allowable**

**Cell**

**Name**

**Value**

**Price**

**R.H. Side**

**Increase**

**Decrease**

$E$3

Assembly (hr/unit)

563.33

0.00

600

1E+30

36.67

$E$4

Paint (hr/unit)

300.00

33.33

300

39.29

175

$E$5

Inspect (hr/unit)

100.00

145.83

100

12.94

40

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.

Answer

**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**

**Cost/oz**

**protien (%)**

**fat (%)**

Partner's Choice

$0.20

45

20

Feline Excel

$0.15

15

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 fortyfive cents) should be written as 9.45*

Answer

**Question 34**

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

MAX + 8x2

s.t. x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45

x1, x2 ≥ 0 and integer

Answer

**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. *

Answer

**Question 36**

Mr. Sartre 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

38

25

33

10

B

10

15

20

85

C

20

100

20

-25

D

25

25

100

25

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*

Answer

**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. *

Answer

**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. *

Answer

**Question 39**

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

Month

Actual Demand

May

33

June

32

July

39

August

37

The forecasted demand for May, June, July and August were 25, 30, 33, and 38 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*

Answer

**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.X