A new Italian restaurant called the Olive Grove is opening in a number of 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 also 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.

a. Select the correct GP model for this problem assuming 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.) Assume the marketing manager wants to minimize the maximum percentage deviation from either goal.

Let X₁ represent Number of magazine ads. Let X₂ represent Number of TV ads.

I	MAX	Q
	ST	250X1 + 1,200X2 + d1- - d1+ = 17,250
		2,000X1 + 12,000X2 + d2- - d2+ = 12,000
		X1 5
		X2 10
		0 di-, di+ Q

II	MAX	Q
	ST	250X1 + 1,200X2 + d1- - d1+ = 12,000
		2,000X1 + 12,000X2 + d2- - d2+ = 17,250
		X1 10
		X2 5
		0 di-, di+ Q

III	MIN	Q
	ST	250X1 + 1,200X2 + d1- - d1+ = 12,000
		12,000X1 + 2,000X2 + d2- - d2+ = 17,250
		X1 5
		X2 10
		0 di-, di+ Q

IV	MIN	Q
	ST	250X1 + 1,200X2 + d1- - d1+ = 17,250
		2,000X1 + 12,000X2 + d2- - d2+ = 12,000
		X1 10
		X2 5
		0 di-, di+ Q

b. Implement your model in a spreadsheet and solve it. How many ads for each type should the manager run?

Magazine
TV

c. What is the minimized maximum percentage deviation from either goal? Round your answer to two decimal places. %