Concept explainers
To calculate: the optimal amount that should be spent on each type of ad and the optimal total audience.
Answer to Problem 60E
The optimal audience will be 250 million for which the budget should be only for newspaper ads.
Explanation of Solution
Given information:
A company has maximum budget of $1000000 for national advertising of an allergy medication. Each TV ad costs $100000 and one page newspaper ad costs $20000. Each TV ad is to be viewed by 20 million viewers, and each newspaper ad is to be seen by 5 million readers. The company’s marketing department recommends that at most 80% of the budget be spent on TV ads.
Calculation:
Let, x be the minutes on TV ads and y be the pages on newspaper ads.
Set up the constraints or inequalities:
Total budget will be
For 80% on TV ads
For 20% on newspaper ads
Objective function is
Graph the inequalities
Evaluate the objective function at each vertex to determine optimal cost.
This means that there should be 0 minutes for TV ads and 10 pages for newspaper so all the budget should go to newspaper ad.
Therefore, TV ads: $0
Newspaper ads: $1000000
This also means that there will be 50 pages allocated
Conclusion:
The optimal audience will be 250 million for which the budget should be only for newspaper ads.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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