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Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessica Martinez, Kelly's campaign
manager during this election, is planning the marketing campaign, and there is some stiff competition. Martinez has
selected four ways to advertise: television ads, radio ads, billboards, and newspaper ads. The costs of these, the
audience reached by each type of ad, and the maximum number of each is shown in the following table:
Type of Ad Cost Per Ad Audience Reached Max Number
TV 800 30,000 10
Radio 400 22,000 10
Billboards 500 24,000 10
Newspaper 100 8,000 10
In addition, Martinez has decided that there should be at least six ads on TV or radio or some combination of those
two. The amount spent on billboards and newspapers together must not exceed the amount spent on TV ads. While
fundraising is still continuing, the monthly budget for advertising has been set at $15,000. How many ads of each
type should be placed to maximize the total number of people reached?
Model
Decision Variables:
Number of TV ads = x
Number of Radio ads = y
Number of Bill board ads = z
Number of Newspaper ads = w
Number of audience reached = N
Objective Function:
Maximize N = 30000x + 22000y + 24000z + 8000w
Constraints:
800x + 400y + 500z + 100w ≤ 15000
x+y≥6
500z + 100w ≤ 800x or -800x + 500z + 100w ≤ 0
0 ≤ x ≤ 10
0 ≤ y ≤ 10
0 ≤ z ≤ 10
0 ≤ w ≤ 10
x, y, z, w all integers
Results from QM for Windows
Optimal Solution:
Number of TV ads = 7
Number of Radio ads = 10
Number of Bill board ads = 9
Number of Newspaper ads = 9
Number of audience reached = 718000