Question

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? please do it on a excel sheet

Answer 1

Let X1= the number of radio ads purchased

X2= the number of television ads purchased

Maximize 3,000X1+ 7,000X2 (maximize exposure)

Subject to: 200X1+ 500 X2 ≤ 40,000 (budget constraint)

X1 ≥ 10 (at least 10 radio ads purchased)

X2 ≥ 10 (at least 10 television ads purchased)

X1 ≥ X2 (# of radio ads ≥ # of television ads)

   X1, X2 ≥ 0 (non-negativity constraints)

For solution purposes, the fourth constraint would be rewritten as:

X1− X2 ≥ 0

Optimal Solution: X1 = 175 X2 = 10 Exposure = 595,000 people