Ch 3

The ABC Co. is considering a new consumer product. They believe that the XYZ Co.

may come out with a competing product. If ABC adds an assembly line for the product

and XYZ does not follow with a competitive product, their expected profit is $40,000;

if they add an assembly line and XYZ does follow, they still expect a $10,000 profit.

If ABC adds a new plant addition and XYZ does not produce a competitive product,

they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a

loss of $100,000. For what value of probability that XYZ will offer a competing product

will ABC be indifferent between the alternatives?

Answer: Let X = probability XYZ offers a competing product. Then:

EMV (assembly line) = $10,000∗X + $40,000∗(1-X)

EMV (addition) = -$100,000∗X + $600,000∗(1-X)

or:

$10,000∗X + $40,000∗(1-X) = -$100,000*X + $600,000∗(1-X) or:

$10,000∗X – $40,000∗X + $40,000 = -$100,000∗X -$600,000∗X + $600,000

-$30,000∗X + $700,000∗X = $600,000 – $40,000

$670,000∗X = $560,000

X = $560,000/$670,000 = 0.836

If the probability that XYZ will offer a competing product is estimated to be 0.836, then

ABC will be indifferent between the two alternatives. If the probability that XYZ will

offer a competing product is estimated to be less than 0.836, then ABC should invest in

the addition.

Ch 9

SE Appliances manufacturers refrigerators in Richmond, Charlotte, and Atlanta.

Refrigerators then must be shipped to meet demand in Washington, New York, and

Miami. The table below lists the shipping costs, supply, and demand information.

How many units should be shipped from each plant to each retail store in order to

minimize shipping costs?

Answer: Ship 1000 units from Richmond to New York, 1000 units from Charlotte to

Washington, 800 units from Atlanta to New York, and 1200 units from Atlanta to

Miami, with the 500 from Charlotte to the Dummy unshipped.

Ch 12

Consider the tasks, durations, and predecessor relationships in the following network.

Draw the network and answer the questions that follow.

Activity

Immediate

Optimistic

Most Likely

Pessimistic

Predecessors)

(Weeks)

(Weeks)

(Weeks)

A

—

4

7

10

B

A

2

8

20

C

A

8

12

16

D

B

1

2

3

E

D, C

6

8

22

F

C

2

3

4

G

F

2

2

2

H

F

6

8

10

I

E, G, H

4

8

12

J

I

1

2

3

(a) What is the expected duration of the project?

(b) What is the probability of completion of the project before week 42?

Answer:

(a) 40

(b) 8079

Ch 13

At the start of football season, the ticket office gets busy the day before the first

game. Customers arrive at the rate of four every ten minutes. A ticket seller can service

a customer in four minutes. Traditionally, there are two ticket sellers working. The

university is considering an automated ticket machine similar to the airlines’ e-ticket

system. The automated ticket machine can service a customer in 2 minutes.

(a)

What is the average length of the queue for the in-person model?

(b)

What is the average length of the queue for the automated system model?

(c)

What is the average time in the system for the in-person model?

(d)

What is the average time in the system for the automated system model?

(e)

Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour

(amortized over 5 years). The wait time is only $4 per hour because students are patient.

What is the total cost of each model?

Answer:

(a)

Lq = 2.844

(b)

Lq = 1.6

(c)

W = 0.1852 hour or 11.11 minutes

(d)

W = 0.1 hour or 6 minutes

(e)

Total cost (in-person) = (2 ∗ $8/hour) + (24/hour ∗ .1852 hours) ($4/hour) =

$33.78

Total cost (automated) = (1 ∗ $20/hour) + (24/hour ∗ .1 hour) ($4/hour) = $29.60

Ch 14

A certain grocery store has created the following tables of intervals of random numbers

with regard to the number of people who arrive at its three checkout stands ready to

check out, and the time it takes to check out the individuals. Simulate the utilization

rate of the three checkout stands over four minutes using the following random numbers

for arrivals: 07, 60, 49, and 95. Use the following random numbers for service: 77, 76,

51, and 16. Describe the results at the end of the four-minute period.

Arrivals Interval of Service Time Interval of

Random #s

Random #s

0

01-30

1

01-10

1

31-80

2

11-40

2

81-00

3

41-80

4

81-00

Answer:

t = RN = Arrival # RN = Service Time =

0

07

0

01-10

1

60

1

77

11-40

2

49

1

76

41-80

3

95

2

51

81-00

16

Note: The first customer arrives at minute 1 and exits at minute 4; the second customer

enters at minute 2 and exits at minute 5. A third and fourth customer enter at minute 3.

There is one server open, so customer four will wait for one minute until minute 4 when

the first customer exits.

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