Question

K

A deli owner has room for 55 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total
of 400 oz of cheese. If 5-oz containers sell for $9 and 10-oz containers sell for $17, how many of each should he sell to
maximize his revenue? What is his maximum revenue?
He should sell 5-oz containers and 10-oz containers to maximize his revenue.

Answer 1

$630

Explanation:

This problem can be solved using linear programming. Let x be the number of 5-oz containers and y be the number of 10-oz containers. The constraints are:

x + y = 55 (total number of containers)

5x + 10y = 400 (total amount of cheese in ounces)

x >= 0, y >= 0 (containers must be non-negative)

The objective is to maximize the revenue, which is given by 9x + 17y.

Using a linear programming solver, we find that the maximum revenue is obtained when x = 40 and y = 15. The maximum revenue is 9x + 17y = 9 * 40 + 17 * 15 = $630.

So, the deli owner should sell 40 5-oz containers and 15 10-oz containers to maximize his revenue, which is $630.