A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must
be used. Also, the number of radio ads must be at least as great as the number of television ads.

How many ads of each type should be used? How many people will this reach?

Question

16-06-2024
Engineering

Answered

A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must
be used. Also, the number of radio ads must be at least as great as the number of television ads.

How many ads of each type should be used? How many people will this reach?

Answer :

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scpdude12301 scpdude12301 · Answer 1 · 2024-06-16T14:59:50-04:00

Answer:

To determine the number of ads of each type that should be used to reach as many people as possible while adhering to the given constraints, we can use linear programming. The objective function is to maximize the number of people reached, subject to the constraints that at least 10 ads of each type must be used and the number of radio ads must be at least as great as the number of television ads.We can represent the problem with the following mathematical model:Maximize:

3000r + 7000t

Subject to:

r >= 10

t >= 10

r >= t