Chapter 8.6, Problem 24PE

A sporting goods store sells two types of exercise bikes. The deluxe model costs the store $\text{\$}400$ from the manufacturer and the standard model costs the store $\text{\$}300$ from the manufacturer. The profit that the store makes on the deluxe model is $\$180$ and the profit on the standard model is $\$120$ . The monthly demand for exercise bikes is at most $30$ . Furthermore, the store manager does not want to spend more than $\text{\$}9600$ on inventory for exercise bikes.

a. Determine the number of deluxe models and the number of standard models that the store should have in its inventory each month to maximize profit. (Assume that all exercise bikes in inventory are sold.)

b. What is the maximum profit?

c. If the profit on the deluxe bikes were $\text{\$}150$ and the profit on the standard bikes remained the same, how many of each should the store have to maximize profit?