Sending attachments now. Please do all questions highlighted yellow. I will samples of excel and tutorials upon request.Problem 4-17 Just answer

Frandec Company manufactures, assembles, and rebuilds material handling equipment used in

warehouses and distribution centers. One product, called a Liftmaster, is assembled from four

components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for

5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but

the frames, supports, and straps may be either manufactured by the company or purchased from an

outside supplier. Manufacturing and purchase costs per unit are shown.

Component

Frame

Support

Strap

Manufacturing Cost

$38.00

$11.50

$ 6.50

Purchase Cost

$51.00

$15.00

$ 7.50

Three departments are involved in the production of these components. The time (in minutes per unit)

required to process each component in each department and the available capacity (in hours) for the

three departments are as follows:

Department

Component

Frame

Support

Strap

Capacity (hours)

Cutting

3.5

1.3

0.8

350

Milling

2.2

1.7

—

420

Shaping

3.1

2 .6

1.7

680

a. Formulate and solve a linear programming model for this make-or-buy application. How many of each

component should be manufactured and how many should be purchased?

b. What is the total cost of the manufacturing and purchasing plan?

c. How many hours of production time are used in each department?

d. How much should Frandec be willing to pay for an additional hour of time in the shaping department?

e. Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its

position by pursuing this opportunity? Why or why not?

a.The optimal solution is to manufacture 5,000 frames, 2,692.31 supports, and 0 straps; and to purchase

0 frames, 7307.69 supports, and 5,000 straps.b.The total cost is $368076.9 c.The solution calls for 350

hours of cutting time, 259.62 hours of milling time, and 375 hours of shaping timed. Because this last

requirement is not binding, Frandec should not pay anything for an additional hour of time in the

shaping department. e.The shadow price of the frame constraint is $47. Therefore, Frandec would

benefit from purchasing frames if they are available for $45. That would be true up to a maximum

purchase of 2714:3 units, which is the allowable decrease on that shadow price.

Problem 7-21

The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance

premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in Figure

7.13; the openings between the rooms are numbered 1 through 13. A security ﬁrm proposed that twoway cameras be installed at some room openings. Each camera has the ability to monitor the two rooms

between which the camera is located. For example, if a camera were located at opening number 4,

rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be

covered; and so on. Management decided not to locate a camera system at the entrance to the display

rooms. The objective is to provide security coverage for all eight rooms using the minimum number of

two-way cameras.

a. Formulate a 0-1 integer linear programming model that will enable Bayside’s management to

determine the locations for the camera systems.

b. Solve the model formulated in part (a) to determine how many two-way cameras to purchase and

where they should be located.

c. Suppose that management wants to provide additional security coverage for room 7. Speciﬁcally,

management wants room 7 to be covered by two cameras. How would your model formulated in part

(a) have to change to accommodate this policy restriction?

d. With the policy restriction speciﬁed in part (c), determine how many two-way camera systems will

need to be purchased and where they will be located.

Figure 7-13 below

13-4

4. The following proﬁt payoff table was presented in Problem 1. Suppose that the decision maker

obtained the probability assessments P(s1) 0.65, P(s2) 0.15, and P(s3) 0.20. Use the expected value

approach to determine the optimal decision.

State of Nature

Decision Alternative

s1

s2

s3

d1

250

100

25

d2

100

100

75

13-18

Dante Development Corporation is considering bidding on a contract for a new ofﬁce building complex.

Figure 13.17 shows the decision tree prepared by one of Dante’s analysts. At node 1, the company must

decide whether to bid on the contract. The cost of preparing the bid is $200,000. The upper branch from

node 2 shows that the company has a 0.8 probability of winning the contract if it submits a bid. If the

company wins the bid, it will have to pay $2,000,000 to become a partner in the project. Node 3 shows

that the company will then consider doing a market research study to forecast demand for the ofﬁce

units prior to beginning construction. The cost of this study is $150,000. Node 4 is a chance node

showing the possible outcomes of the market research study. Nodes 5, 6, and 7 are similar in that they

are the decision nodes for Dante to either build the ofﬁce complex or sell the rights in the project to

another developer. The decision to build the complex will result in an income of $5,000,000 if demand is

high and $3,000,000 if demand is moderate. If Dante chooses to sell its rights in the project to another

developer, income from the sale is estimated to be $3,500,000. The probabilities shown at nodes 4, 8,

and 9 are based on the projected outcomes of the market research study. a. Verify Dante’s proﬁt

projections shown at the ending branches of the decision tree by calculating the payoffs of $2,650,000

and $650,000 for ﬁrst two outcomes. b. What is the optimal decision strategy for Dante, and what is the

expected proﬁt for this project? c. What would the cost of the market research study have to be before

Dante would change its decision about the market research study? d. Develop a risk proﬁle for Dante.

13-24

To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona

preferred to use the somewhat longer but more consistent Queen City Avenue. Although Jerry preferred

the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the

expressway had a trafﬁc jam. The following payoff table provides the one-way time estimate in minutes

for traveling to or from work:

Based on their experience with trafﬁc problems, Rona and Jerry agreed on a 0.15 probability that the

expressway would be jammed. In addition, they agreed that weather seemed to affect the trafﬁc

conditions on the expressway. Let

C = clear

O=

overcast

R = rain

The following conditional probabilities apply:

P(C ƒ s1) = 0.8

P(O ƒ s1) = 0.2

P(C ƒ s2 ) = 0.1

P(R ƒ s1) = 0.0

P(R ƒ s2 ) = 0.6

P(O ƒ s2 ) = 0.3

a. Use Bayes’ theorem for probability revision to compute the probability of each weather condition and

the conditional probability of the expressway open s1 or jammed s2 given each weather condition.

b. Show the decision tree for this problem.

c. What is the optimal decision strategy, and what is the expected travel time?

15-12

Corporate triple A bond interest rates for 12 consecutive months follow: 9.5 9.3 9.4 9.6 9.8 9.7 9.8

10.5 9.9 9.7 9.6 9.6

a. Construct a time series plot. What type of pattern exists in the data?

b. Develop three-month and four-month moving averages for this time series. Does the three-month or

four-month moving average provide the better forecasts based on MSE? Explain.

c. What is the moving average forecast for the next month?

15-18

The following table reports the percentage of stocks in a portfolio for nine quarters from 2007 to 2009:

a. Construct a time series plot. What type of pattern exists in the data?

b. Use exponential smoothing to forecast this time series. Using Excel Solver or LINGO ﬁnd the value of

a that minimizes the sum of squared error.

c. What is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009?

15-26

Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern

United States. Using a very aggressive marketing strategy they have been able to increase their annual

revenue by approximately $10 million over the past 10 years. But, increased competition has slowed

their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10

years is shown below.

a. Construct a time series plot. Comment on the appropriateness of a linear trend. b. Using Excel

Solver or LINGO, develop a quadratic trend equation that can be used to forecast revenue. c.

Using the trend equation developed in part

b. (b), forecast revenue in year 11.

9-15

Doug Casey is in charge of planning and coordinating next spring’s sales management training program

for his company. Doug listed the following activity information for this project:

a. Draw a project network.

b. Prepare an activity schedule.

c. What are the critical activities and what is the expected project completion time?

d. If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled

meeting date should he begin working on the project?

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