How many ads of each type should be placed to maximize the total number of people reached?

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?

Answer

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