Question

A department store chain has up to $22,000 to spend on television advertising for a sale. All ads will be placed with one television station, where a 30-second ad costs $1,000 on daytime TV and is viewed by 14,000 potential customers, $2,000 on prime-time TV and is viewed by 24,000 potential customers, and $1,500 on late-night TV and is viewed by 18,000 potential customers. The television station will not accept a total of more than 20 ads in all three time periods. How many ads should be placed in each time period in order to maximize the number of potential customers who will see the ads? How many potential customers will see the ads? (Ignore repeated viewings of the ad by the same potential customer.) Include an interpretation of any nonzero slack variables in the optimal solution. Select the correct choice below and fill in any answer boxes present in your choice. O A. The maximum number of potential customers who see the ads is B. There is no way to maximize the number of potential customers. people when daytime ads, prime-time ads, and late-night ads are placed.

Answer 1

To maximize the number of potential customers who will see the ads, we need to find the number of ads that should be placed in each time period. This is a linear programming problem that can be solved using linear programming techniques.

Step-by-step explanation:

To maximize the number of potential customers who will see the ads, we need to find the number of ads that should be placed in each time period. Let's denote the number of daytime ads as x, prime-time ads as y, and late-night ads as z.

We need to maximize the total number of potential customers, which is 14,000x + 24,000y + 18,000z. However, there are constraints that need to be considered:

1. The total cost of ads cannot exceed $22,000, which gives us the inequality 1,000x + 2,000y + 1,500z ≤ 22,000.
2. The total number of ads in all three time periods cannot exceed 20, which gives us the inequality x + y + z ≤ 20.
3. The number of ads in each time period should be non-negative, so x, y, and z ≥ 0.

This is a linear programming problem that can be solved using linear programming techniques.