Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessi
ID: 3439362 • Letter: E
Question
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
Type of Ad Cost per Ad Audience Reached/Ad Maximum Number TV $800 30,000 10 Radio $400 22,000 10 Billboards $500 24,000 10 Newspapers $100 8,000 10Explanation / Answer
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.
AD Type Costs Audience reach Number of ads Max. Ads TV 800 30000 6 10 Radio 400 22000 10 10 BillBoard 500 24000 10 10 NewsPapers 100 8000 10 10 Total Audience 720000 Total Costs 14800 Tv + Radio Ads 16Related Questions
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