A committee in charge of promoting a Ladies Professional Golf Association tournament is trying to determine how best to advertise the event during the two weeks prior to the tournament. The committee obtained the following information about the three advertising media they are considering using:

The last column in this table shows the maximum number of advertisements that can be run during the next two weeks; these values should be treated as constraints. The committee established the following goals for the campaign:
Priority Level 1 Goal
Goal 1: Reach at least 4 million people.
Priority Level 2 Goal
Goal 2: The number of television advertisements should be at least 30% of the total number of advertisements.
Priority Level 3 Goal
Goal 3: The number of radio advertisements should not exceed 20% of the total number of advertisements.
Priority Level 4 Goal
Goal 4: Limit the total amount spent for advertising to $20,000.
a. Formulate a goal programming model for this problem.
b. Use the goal programming computer procedure illustrated in Section 14.2 to solve the model formulated in part(a).

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Category TV Radio Newspaper Audience Reached per Advertisement 200,000 50,000 100,000 Cost per Advertisement $2500 $ 400 $ 500 Maximum Number of Advertisements 10 15 20