Chapter 6.2, Problem 45E

In Problems 41-56, construct a mathematical model in the form of a linear programming problem. (The answer in the back of the book for these application problems include the model.) Then solve the problem using the simplex method. Include an interpretation of any nonzero slack variables in the optimal solution.

Advertising. A department store has up to $\text{\$}20,000$ to spend on television advertising for a sale, All ads will be places with one television station. A $30$ -second ad costs $\text{\$}1,000$ on daytime TV and is viewed by $14,000$ potential customers, $\text{\$}2,000$ on prime-time TV and is viewed by $24,000$ potential customers, and $\text{\$}1,500$ on late-night TV and is viewed by $18,000$ potential customers. The television station will not accept a total of more than $15$ 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.)