Questions: If the store wants to maximize exposure, it should use: ? newspaper ads, ? radio ads, and ? TV ads How many people will be reached in total?

Solution Steps

To solve this problem, we need to maximize the total exposure given the constraints on the budget and the number of ads. We can set up a linear programming problem where the objective function is to maximize the total number of people reached. The constraints will include the budget limit and the maximum number of ads allowed for each type.

1. Define variables for the number of newspaper and TV ads.
2. Set up the objective function to maximize the total exposure.
3. Add constraints for the budget and the maximum number of ads.
4. Use a linear programming solver to find the optimal number of each type of ad.

Let \( x \) be the number of newspaper ads and \( y \) be the number of TV ads.

The objective is to maximize the total exposure, given by: \[ \text{Total Exposure} = 3500x + 20000y \]

The constraints based on the budget and limits are:

1. Budget constraint: \( 100x + 500y \leq 3000 \)
2. Newspaper ad limit: \( x \leq 40 \)
3. TV ad limit: \( y \leq 12 \)

From the solution, we find:

• \( x = 0 \) (number of newspaper ads)
• \( y = 6 \) (number of TV ads)

Substituting the values into the total exposure formula: \[ \text{Total Exposure} = 3500(0) + 20000(6) = 120000 \]

Final Answer