Question

2) 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 available are shown in the following table: Type of AD Maximum number Cost per AD $800 $400 $500 $100 TV Social media Billboards Newspapers Audience reached/AD 30,000 22,000 24,000 8,000 10 10 In addition, Martinez has decided that there should be at least six ads on TV or social media or some combination of those two. The amount spent on billboards and newspaper 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? • Formulate the problem as a linear program.

Answer 1

Let the total no. of ads to be published in each category be A,B,C & D respectively.

NOW, as there is need to maximize the reach to audience there should be the objective function denoted by Z.

Z=30000A+22000B+24000C+8000D

Subject to,

Constraints as follows:

A+B ≥ 6

800A ≥ 500C+100D

800A+400B+500C+100D ≤ 15000

A,B,C,D ≤ 10

A,B,C,D ≥0 (non negative constraints)

The above is the solution for linear program.