# Quantitative Management Analysis

See attached file for charts and tables.

1. Given that the MAD for the following forecast is 2.5, what is the actual

value in period 2?

Period Forecast Actual

1 100 95

2 110

3 120 123

4 130 130

(a) 120

(b) 98

(c) 108

(d) 115

(e) none of the above

2. Assume that you have tried three different forecasting models. For the

first, the MAD = 2.5, for the second, the MSE = 10.5, and for the third, the

MAPE = 2.7. We can then say:

(a) the third method is the best.

(b) the second method is the best.

(c) methods one and three are preferable to method two.

(d) method two is least preferred.

(e) none of the above

3. Daily demand for newspapers for the last 10 days has been as follows: 12,

13, 16, 15, 12, 18, 14, 12, 13, 15. Forecast sales for the next day using a

two-day moving average.

(a) 14

(b) 13

(c) 15

(d) 28

(e) none of the above

4. An exponential smoothing model having a large

(a) is more responsive to recent demand changes.

(b) is less responsive to recent demand.

(c) places emphasis on the past demand data.

(d) is always the most effective weighting scheme.

(e) is not a time-series model.

5. Enrollment in a particular class for the last four semesters has been 120, 126, 110, and 130. Develop a forecast of enrollment next semester using exponential smoothing with an alpha = 0.2. Assume that an initial forecast for the first semester was 120 (so the forecast and the actual were the same).

(a) 118.96

(b) 121.17

(c) 130

(d) 120

(e) none of the above

6. Which of the following is not a characteristic of trend projections?

(a) The variable being predicted is the Y variable.

(b) Time is the X variable

(c) It is useful for predicting the value of one variable based on time trend.

(d) It is helpful for determining if time is causing the dependent variable.

(e) none of the above

7. In making inventory decisions, the purpose of the basic model is to

(a) minimize customer dissatisfaction.

(b) minimize stock on hand.

(c) minimize carrying costs.

(d) minimize ordering costs.

(e) minimize the sum of carrying costs and ordering costs.

8. Mark Achin sells 3,600 electric motors each year. The cost of these is $200 each, and demand is constant throughout the year. The cost of placing an order is $40, while the holding cost is $20 per unit per year. There are 360 working days per year and the lead-time is 5 days. If Mark orders 200 units each time he places an order, what would his average inventory be (in units)?

(a) 100

(b) 200

(c) 60

(d) 120

(e) none of the above

9. Andre Candess manages an office supply store. One product in the store is computer paper. Andre knows that 10,000 boxes will be sold this year at a constant rate throughout the year. There are 250 working days per year and the lead-time is 3 days. The cost of placing an order is $30, while the holding cost is $15 per box per year. How many units should Andre order each time to minimize his annual inventory cost?

(a) 200

(b) 400

(c) 500

(d) 100

(e) none of the above

10. Daniel Trumpe has computed the EOQ for a product he sells to be 400 units. However, due to recent events he has a cash flow problem. Therefore, he orders only 100 units each time he places an order. Which of the following is true for this situation?

(a) Total ordering cost will be higher than total holding cost.

(b) Total ordering cost will be lower than total holding cost.

(c) Total ordering cost will equal total holding cost.

(d) Nothing can be determined without more information.

(e) none of the above

11. Demand for a product is constant, but the lead time fluctuates. The demand during the lead time is normally distributed with a mean of 40 and a standard deviation of 4. If they have calculated a reorder point of 45.12 units, what service level are they assuming?

(a) 85 percent

(b) 90 percent

(c) 95 percent

(d) 97.5 percent

(e) none of the above

12. Judith Thompson is the manager of the student center cafeteria. She is introducing pizza as a menu item. The pizza is ordered frozen from a local pizza establishment and baked at the cafeteria. Judith anticipates a weekly demand of 10 pizzas. The cafeteria is open 45 weeks a

year, 5 days a week. The ordering cost is $15 and the holding cost is $0.40 per pizza per year. What is the optimal number of pizzas Judith should order?

(a) 184 pizzas

(b) 9 pizzas

(c) 5 pizzas

(d) 28 pizzas

(e) none of the above

13. Judith Thompson, the manager of the student center cafeteria, has added pizza to the menu. The pizza is ordered frozen from a local pizza establishment and baked at the cafeteria. Judith anticipates a weekly demand of 10 pizzas. The cafeteria is open 45 weeks a year, 5 days a week. The ordering cost if $15 and the holding cost is $0.40 per pizza per year. The pizza vendor has a 4-day lead-time and Judith wants to maintain 1 pizza for safety stock. What is the optimal reorder point?

(a) 10

(b) 8

(c) 4

(d) 9

(e) none of the above

14. Judith Thompson, the student cafeteria manager, has decided to keep pizza as a permanent menu item after 3 successful months. She has entered discussions with the local pizza supplier to obtain a quantity discount. Currently, each pizza costs $4.75; however, if Judith purchases at least 225 pizzas at a time, their cost is $4.25 each. How much money can Judith save by ordering 225 pizzas at a time?

(a) Judith will not save any money

(b) $258.48

(c) $223.48

(d) $260.00

(e) none of the above

15. A feasible solution to a linear programming problem

(a) must satisfy all of the problem's constraints simultaneously.

(b) need not satisfy all of the constraints, only the non-

negativity constraints.

(c) must be a corner point of the feasible region.

(d) must give the maximum possible profit.

16. Consider the following linear programming problem:

Maximize 12X + 10Y

Subject to: 4X + 3Y 480

2X + 3Y 360

all variables 0

The maximum possible value for the objective function is

(a) 360.

(b) 480.

(c) 1520.

(d) 1560.

(e) none of the above

17. Consider the following linear programming problem:

Maximize 4X + 10Y

Subject to: 3X + 4Y 480

4X + 2Y 360

all variables 0

The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function?

(a) 1032

(b) 1200

(c) 360

(d) 1600

(e) none of the above

18. Consider the following linear programming problem:

Maximize 5X + 6Y

Subject to: 4X + 2Y 420

1X + 2Y 120

all variables 0

Which of the following points (X,Y) is not a feasible corner point?

(a) (0,60)

(b) (105,0)

(c) (120,0)

(d) (100,10)

(e) none of the above

19. Two models of a product - Regular (X) and Deluxe (Y) - are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit = 50X + 60Y

Subject to: 8X + 10Y 800 (labor hours)

X + Y 120 (total units demanded)

4X +10Y 500 (raw materials)

X, Y 0

The optimal solution is X=100, Y=0.

Which of these constraints is redundant?

(a) the first constraint

(b) the second constraint

(c) the third constraint

(d) all of the above

(e) none of the above

20. Consider the following linear programming problem:

Maximize 20X + 30Y

Subject to X + Y 80

8X + 9Y 600

3X + 2Y 400

X, Y 0

This is a special case of a linear programming problem in which

(a) there is no feasible solution.

(b) there is a redundant constraint.

(c) there are multiple optimal solutions.

(d) this cannot be solved graphically.

(e) none of the above

21. Deleting a constraint from a linear programming (maximization) problem may result in, but is not limited to,

(a) a decrease in the value of the objective function.

(b) an increase in the value of the objective function.

(c) no change to the objective function.

(d) either (c) or (a) depending on the constraint.

(e) either (c) or (b) depending on the constraint.

22. In order for a linear programming problem to have a unique solution, the solution must exist

(a) at the intersection of the non-negativity constraints.

(b) at the intersection of a non-negativity constraint and a

resource constraint.

(c) at the intersection of the objective function and a constraint.

(d) at the intersection of two or more constraints.

(e) none of the above

Table 10-3

To==> 1 2 3 Dummy Supply

From

A

| 10

| 8

80 | 12

| 0

20

100

B | 6

120 | 7

| 4

30 | 0

150

C | 10

| 9

| 6

170 | 0

80

250

Demand

120

80

200

100

The following cell improvements are provided for Table 10-3

Cell Improvement Index

A1 +2

A3 +6

B2 +1

B-Dummy +2

C1 +2

C2 +1

23.. The cell improvement indices for Table 10-3 suggest that the

optimal solution has been found. Based on this solution, how

many units would actually be sent from source C?

(a) 10

(b) 170

(c) 180

(d) 250

(e) none of the above

24. A company must assign mechanics to each of four jobs. The time involved varies according to individual abilities. Table 10-4 shows how many minutes it takes each mechanic to perform each job. This was solved using the Hungarian method. Table 10-5 shows the solution.

Table 10-4

Job

1 2 3 4

Worker A 4 6 5 4

B 3 5 4 7

C 5 6 5 4

D 7 5 5 6

Table 10-5

Final Table Job

1 2 3 4

Worker A 0 1 0 0

B 0 1 0 4

C 1 1 0 0

D 3 0 0 2

If optimal assignments are made, how many total minutes would be required to complete the jobs?

(a) 0

(b) 4

(c) 17

(d) 20

(e) none of the above

Table 10-16

To==> 1 2 3 Dummy Supply

From

A

| 10

| 8

80 | 12

| 0

20

100

B | 6

120 | 7

40 | 4

30 | 0

150

C | 10

| 9

10 | 6

170 | 0

80

250

Demand

120

80

200

100

25. What is wrong with Table 10-16?

(a) The solution is infeasible.

(b) The solution is degenerate.

(c) The solution is unbounded.

(d) Nothing is wrong.

(e) The solution is inefficient in that it is possible to use fewer routes.

Table 10-23

To==> 1 2 3 Supply

From

A | 6

| 4

| 5

200

B | 8

| 6

| 7

300

C | 5

| 5

| 6

300

Demand

400

200

100

26. Table 10-23 provides information about a transportation problem.

This problem is

(a) unbounded.

(b) unbalanced.

(c) infeasible.

(d) all of the above

(e) none of the above

27. Given Table 10-31, the final table for an assignment problem, which assignment would you make first?

(a) worker A

(b) worker B

(c) worker C

(d) Either worker B or worker C

(e) Either worker A or worker C

Table 10-31 Job (Time in Minutes)

1 2 3 4

Worker A 0 1 2 3

B 0 0 0 1

C 2 2 5 0

D 4 0 0 2

28. Given Table 10-32, the final assignment table for a problem, who would be assigned to job 3?

(a) worker A

(b) worker B

(c) worker C

(d) worker B or worker D

(e) none of the above

Table 10-32 Job (Time in Minutes)

1 2 3 4

Worker A 0 1 2 3

B 0 0 0 1

C 2 2 5 0

D 4 0 0 2.

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#### Solution Summary

The solution provides a quantitative management analysis.

Quantitative Analysis for Management (10th ed.)

From historical data, Harry's Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line.

Assuming Poisson arrivals and exponential service times, find the

(a) average number of cars inline.

(b) average time a car waits before it is washed.

(c) average time a car spends in the service system.

(d) utilization rate of the car wash.

(e) probability that no cars are in the system.