# Mat 540 final exam latest

MAT 540 FINAL EXAM THREE VERSIONS (120 QUESTIONS)

Question 1

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

True
False
Question 2

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

True
False
Question 3

True
False
Question 4

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

True
False

Question 5

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

True
False
Question 6

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.

True
False
Question 7

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

Breakeven point decreases

Breakeven point increases

Breakeven point does not change

The revenue per unit goes down

Question 8

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

exhaustive

dependent

independent

mutually exclusive

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:

12

55

57

69

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.

The conservative (maximin) strategy is:

Rent

Lease

Brisk.

Question 11

The probability of observing x
successes in a fixed number of trials is a problem related to

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

B = 225, M = 0

B = 0, M = 225

B = 150, M = 75

B = 75, M = 150

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 objective function?

Max Z = 75B + 85M

Max Z = 85B + 75M

100B + 50M  ≤  25000

100B + 50M  ≥ 25000

100B + 80M  ≤  18000

100B + 80M  ≥  18000

Question 14

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?

mix/mold

kiln

paint and seal

Cannot tell from the information provided

Question 15

Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to        8x + 4y ≥ 64
2x + 4y ≥ 32
y ≥ 2

What is the sensitivity range for the third constraint, y ≥ 2?

0 to 4

2 to 5.33

0 to 5.33

4 to 6.33

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:

.5A + .75B = 20

.3B = 20

.3 B≤ 20

.3B ≥ 20

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.
An appropriate part of the model would be

15X1 + 47.25X2 +110 X3 ≤ 50,000

MAX   Z =15X1 + 47.25X2 + 110X3

X1 + X2 +X3 ≤ 50,000

MAX    Z = 50(15)X1 + 50 (47.25)X2 + 50 (110)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.

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.

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

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 supplied by DC 1 is:

4X1A + 6X1B + 8X1C ≤ 500

4X1A + 6X1B + 8X1C = 500

X1A + X1B + X1C ≤ 500

X1A + X1B + X1C ≥500

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:

mutually exclusive

independent

controlled by the central limit theorem

all of the above

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.

0.03

0.05

0.07

0.09

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 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?

23

24

22

25

Question 25

Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?

Trend only

Trend plus seasonal

Trend plus irregular

Seasonal

Question 26

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

0

1

2

3

Question 27

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

Longer-period, shorter-period

Shorter-period, longer-period

Longer-period, longer-period

Shorter-period, shorter-period

Question 28

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 29

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 30

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).

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

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.

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

Question 33

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

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

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

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.

Investment Economic Conditions
Poor
(S1) Average
(S2) Good
(S3) Excellent
(S4)
A  18 25 50 80
B 19 100 50 75
C  100 26 120 60
D 20 27 50 240

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 Sales Forecast
2003 7 7
2004 8 8.5
2005 12 10.5
2006 14 13
2007 16 15
2008 18 16

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

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.

Final Draft of MAT 540 Final

1. Which of the following could be a linear programming objective function? (Points : 5)
Z = 1A + 2BC + 3D
Z = 1A + 2B + 3C + 4D
Z = 1A + 2B / C + 3D
Z = 1A + 2B2 + 3D
all of the above

2. Which of the following could not be a linear programming problem constraint? (Points : 5)
1A + 2B
1A + 2B = 3
1A + 2B LTOREQ 3
1A + 2B GTOREQ 3

3. Types of integer programming models are _____________. (Points : 5)
total
0 – 1
mixed
all of the above

4. 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. If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of (Points : 5)
malt only
wheat only
both malt and wheat
neither malt nor wheat

5. The reduced cost (shadow price) for a positive decision variable is 0.
(Points : 5)
True
False

6. Decision variables (Points : 5)
measure the objective function
measure how much or how many items to produce, purchase, hire, etc.
always exist for each constraint
measure the values of each constraint

7. A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in the: (Points : 5)
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

8. Decision models are mathematical symbols representing levels of activity.
(Points : 5)
True
False

9. The integer programming model for a transportation problem has constraints for supply at each source and demand at each destination.
(Points : 5)
True
False

10. In a transportation problem, items are allocated from sources to destinations (Points : 5)
at a maximum cost
at a minimum cost
at a minimum profit
at a minimum revenue

11. In a media selection problem, the estimated number of customers reached by a given media would generally be specified in the _________________. Even if these media exposure estimates are correct, using media exposure as a surrogate does not lead to maximization of ______________. (Points : 5)
problem constraints, sales
problem constraints, profits
objective function, profits
problem output, marginal revenue
problem statement, revenue

12. ____________ solutions are ones that satisfy all the constraints simultaneously. (Points : 5)
alternate
feasible
infeasible
optimal
unbounded

13. In a linear programming problem, a valid objective function can be represented as (Points : 5)
Max Z = 5xy
Max Z 5×2 + 2y2
Max 3x + 3y + 1/3z
Min (x1 + x2) / x3

14. The standard form for the computer solution of a linear programming problem requires all variables to the right and all numerical values to the left of the inequality or equality sign
(Points : 5)
True
False

15. Constraints representing fractional relationships such as the production quantity of product 1 must be at least twice as much as the production quantity of products 2, 3 and 4 combined cannot be input into computer software packages because the left side of the inequality does not consist of consists of pure numbers.
(Points : 5)
True
False

16. In a balanced transportation model where supply equals demand, (Points : 5)
all constraints are equalities
none of the constraints are equalities
all constraints are inequalities
all constraints are inequalities

17. The objective function is a linear relationship reflecting the objective of an operation.
(Points : 5)
True
False

18. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are \$0.40, and for a bag of Vinegar chips \$0.50. Which of the following is not a feasible production combination? (Points : 5)
0L and 0V
0L and 1000V
1000L and 0V
0L and 1200V

19. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.
(Points : 5)
True
False

20. 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: (Points : 5)
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

21. In a total integer model, all decision variables have integer solution values.
(Points : 5)
True
False

22. Linear programming is a model consisting of linear relationships representing a firm’s decisions given an objective and resource constraints.
(Points : 5)
True
False

23. When using linear programming model to solve the “diet” problem, the objective is generally to maximize profit.
(Points : 5)
True
False

24. In a balanced transportation model where supply equals demand, all constraints are equalities.
(Points : 5)
True
False

25. In a transportation problem, items are allocated from sources to destinations at a minimum cost.
(Points : 5)
True
False

26. Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150.  Which of the following is not a feasible purchase combination? (Points : 5)
0 big shelves and 200 medium shelves
0 big shelves and 0 medium shelves
150 big shelves and 0 medium shelves
100 big shelves and 100 medium shelves

27. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.
(Points : 5)
True
False

28. In a 0 – 1 integer model, the solution values of the decision variables are 0 or 1.
(Points : 5)
True
False

29. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.
(Points : 5)
True
False

30. The dietician for the local hospital is trying to control the calorie intake of the heart surgery patients. Tonight’s dinner menu could consist of the following food items: chicken, lasagna, pudding, salad, mashed potatoes and jello. The calories per serving for each of these items are as follows: chicken (600), lasagna (700), pudding (300), salad (200), mashed potatoes with gravy (400) and jello (200). If the maximum calorie intake has to be limited to 1200 calories. What is the dinner menu that would result in the highest calorie in take without going over  the total calorie limit of 1200. (Points : 5)
chicken, mashed potatoes and gravy, jello and salad
lasagna, mashed potatoes and gravy, and jello
chicken, mashed potatoes and gravy, and pudding
lasagna, mashed potatoes and gravy, and salad
chicken, mashed potatoes and gravy, and salad

31. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints’ prices.
(Points : 5)
True
False

32. The transportation method assumes that (Points : 5)
the number of rows is equal to the number of columns
there must be at least 2 rows and at least 2 columns
1 and 2
the product of rows minus 1 and columns minus 1 should not be less than the number of completed cells

33. A constraint is a linear relationship representing a restriction on decision making.
(Points : 5)
True
False

34. When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell.

(Points : 5)
True
False

35. The linear programming model for a transportation problem has constraints for supply at each ________ and _________ at each destination. (Points : 5)
destination / source
source / destination
demand / source
source / demand

36. The 3 types of integer programming models are total, 0 – 1, and mixed.
(Points : 5)
True
False

37. In using rounding of a linear programming model to obtain an integer solution, the solution is (Points : 5)
always optimal and feasible
sometimes optimal and feasible
always optimal
always feasible
never optimal and feasible

38. If we use Excel to solve a linear programming problem instead of QM for Windows,
then the data input requirements are likely to be much less tedious and time consuming.

(Points : 5)
True
False

39. In a _______ integer model, some solution values for decision variables are integer and others can be non-integer. (Points : 5)
total
0 – 1
mixed
all of the above

40. Which of the following is not an integer linear programming problem? (Points : 5)
pure integer
mixed integer
0-1integer
continuous

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