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

## MAT 540 Week 11 Final Exam Quiz

• Question 1

5 out of 5 points

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

• Question 2

5 out of 5 points

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

• Question 3

5 out of 5 points

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

• Question 4

5 out of 5 points

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

• Question 5

5 out of 5 points

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

• Question 6

5 out of 5 points

Fractional relationships between variables are not permitted in the standard form of a linear program.

• Question 7

5 out of 5 points

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

• Question 8

5 out of 5 points

Using the minimax regret criterion to make a decision, you

• Question 9

0 out of 5 points

Using the maximin criterion to make a decision, you

• Question 10

5 out of 5 points

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 11

5 out of 5 points

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

• Question 12

0 out of 5 points

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 13

0 out of 5 points

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

5 out of 5 points

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 15

5 out of 5 points

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 16

5 out of 5 points

Compared to transportation LP problems, assignment problems are unique because

• Question 17

5 out of 5 points

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 18

5 out of 5 points

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 19

5 out of 5 points

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

• Question 20

5 out of 5 points

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

• Question 21

0 out of 5 points

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6?

• Question 22

5 out of 5 points

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

0 out of 5 points

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

5 out of 5 points

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

• Question 25

5 out of 5 points

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

5 out of 5 points

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

• Question 27

5 out of 5 points

In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

• Question 28

0 out of 5 points

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).

• Question 29

0 out of 5 points

Suppose that a production process requires a fixed cost of \$50,000. The variable cost per unit is \$10 and the revenue per unit is projected to be \$50. Find the break-even point.

• Question 30

0 out of 5 points

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

5 out of 5 points

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 32

5 out of 5 points

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 33

0 out of 5 points

Kitty 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 (%)

Meow Munch \$0.20 30 10

Feline Feed \$0.15 15 30

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 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

0 out of 5 points

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

Max Z = x1 + 6×2

Subject to: 17×1 + 8×2 ? 136

3×1 + 4×2 ? 36

x1, x2 ? 0 and integer

• Question 35

0 out of 5 points

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

• Question 36

0 out of 5 points

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

0 out of 5 points

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

5 out of 5 points

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

0 out of 5 points

The following sales data are available for 2003-2008 :

Year Sales Forecast

2003 7 9

2004 12 10

2005 14 15

2006 20 22

2007 16 18

2008 25 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

• Question 40

5 out of 5 points

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.