MA/OR 504 Fall2017Homework 3page 1

Homework 3 due Monday Oct. 2

#1.

A new Italian restaurant called the Olive Grove is opening in several locations in the Memphis area. The marketing manager for these stores has a budget of $150,000 to use in advertising and promotions for the new stores. The manager can run magazine ads at a cost of $2,000 each that result in 250,000 exposures each. TV ads result in approximately 1,200,000 exposures each, but cost $12,000 each. The manager wants to run at least five TV ads and ten magazine ads, while maximizing the number of exposures generated by the advertising campaign. But the manager wants to spend no more than $120,000 on magazine and TV advertising so that the remaining $30,000 could be used for other promotional purposes. However, the manager would spend more than $120,000 on advertising if it resulted in a substantial increase in advertising coverage.

  1. Formulate a goal programming model for this problem assuming that the marketing manager has the following goals:

Goal 1: Exposures should be maximized

Goal 2: No more than $120,000 should be spent on advertising

(Note that you will have to determine an appropriate target value for the first goal.)

  1. Implement your model in a spreadsheet and solve it.

c.What is the solution?

d.What changes do you make to your model if the manager wants to spend less on advertising than your solution suggests?

#2.

The Chick’n-Pick’n fast-food chain is considering how to expand its operations. Three types of retail outlets are possible: a lunch counter operation designed for office buildings in downtown areas, an eat-in operation designed for shopping malls, and a stand-alone building with drive-through and sit-down facilities. The following table summarizes the number of jobs, start-up costs, and annual returns associated with each type of operation:

Lunch Counter / Mall / Stand-alone
Jobs / 9 / 17 / 35
Costs / $150,000 / $275,000 / $450,000
Returns / $85,000 / $125,000 / $175,000

The company has $2,000,000 available to pay start-up costs for new operations in the coming year. Additionally, there are five possible sites for lunch counter operations, seven possible mall locations, and three possible stand-alone locations. The company wants to plan its expansion in a way that maximizes annual returns and the number of jobs created.

a.Formulate a multi-objective linear programming (MOLP) model for this problem.

b.Determine the best possible value for each objective in the problem.

c.Implement your model in a spreadsheet and solve it to determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What is the solution?

d.Suppose management considers maximizing returns three times as important as maximizing the number of jobs created. What solution does this suggest?

HW 3 HINTS

#1

a.Let X1 = number of magazine ads, X2 = number of TV ads

MIN Q

ST 250 X1 + 1,200 X2 + - = 17,250

2,000 X1 + 12,000 X2 + - = 120,000

X1 10

X2 5

Xi integer

0 Q

NOTE: Use $150,000 to determine the target value for exposures.

#2

a. LetX1=number of lunch counter units built

X2=number of mall units built

X3=number of standalone units built

MAX85 X1 + 125 X2 + 175 X3(returns)

MAX 9 X1 + 17 X2 + 35 X3(jobs created)

ST 150 X1 + 275 X2 + 450 X3 2,000

0  X1 5

0  X2 7

0  X3 3

Xi integer