Eddie Kelly is running for reelection as mayor of a small to

Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessica Martinez, Kellys 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:

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?

PLEASE SHOW WORK

Solution

This is an optimization problem with the objective to maximise Audience reached under the given constraints.

The constraints are:

Max ad of any type <= 10

TV + Radio ad >= 6

Total Budget <= 15000

Also, the additional constraint should be that the number of ads must be an integer.

Putting all the above constraints in an excel solver we get:

The total out reach here is 720,000 people and the cost is 14,800

You need to have 6 ads in TV, 10 each on radio, bill boards and the news papers.

Hope this helps. Ask if you have any doubts.