Number of Newspaper ads to run is? Correct Number of Radio ads to run is? Maximum target group exposure is?

Question

A company has $8,470 available per month for advertising. Newspaper ads cost $240 each and can't run more than 21 times per month. Radio ads cost $560 each and can't run more than 28 times per month at this price.

Each newspaper ad reaches 6450 potential customers, and each radio ad reaches 7900 potential customers. The company wants to maximize the number of ad exposures to potential customers.

Use n for number of Newspaper advertisements and r for number of Radio advertisements .

Answer 1

For this problem, the easiest approach is determining which form of advertising reaches the most people for the least amount of money and maximizing the number of advertisements use on that form of advertising. We can do that by simply taking the ratio of customers reached to dollars spent per advertisement:

Customers per Advertisement Cost: (# of potential customers) / (Advertisement Cost)

Newspaper: (6450 customers) / ($240 per ad) = 26.88 customers / dollar

Radio: (7900 customers) / ($560 per ad) = 14.11 customers / dollar

Here we can see that while newspaper ads reach fewer people per advertisement, the lower cost makes them more cost-effective, meaning that we should maximize the number of ads run in the newspaper. From the problem statement, we can see that we're limited to 21 ads per month, meaning that we should spend,

Newspaper Advertising Cost -> 21 * $240 = $5040

After spending $5040 on newspaper advertising, we are left with $3430 to spend on radio advertisements. If we divide the money remaining after newspaper advertising by the cost per radio advertisement, we find that we can run an additional 6 radio advertisements ($3430/$560 = 6.125). This means that the company should run 21 newspaper advertisements and 6 radio advertisements.