Problem:

Caroline's quality candy confectionery is famous for fudge, chocolate crèmes, and pralines. Its candy-making equipment is set up to make 100-pound batches at a time. Currently there is a chocolate shortage and the company can get only 120 pounds of chocolate in the next shipment. On a week's run the confectionery's cooking and processing equipment is available for a total of 42 machine hours. During thedame period the employees have a total of 57 work hours available for packaging. A batch of fudge requires 20 pounds of chocolate while a batch of crèmes uses 25 pounds of chocolate. The cooking and processing take 120 minutes for a batch of fudge, 150 minutes for a batch of chocolate crèmes and 200 minutes fora batch of pralines.

Use the simplex method to solve

Required:

1. Determine how many batches of each type of candy the confectionery should make assuming that the profit per pound box is $0.50 on fudge, $0.40 on chocolate cremes and $0.45 onpralines.
2. Find the maximum profit for the week.

Note: Please provide equation and explain comprehensively and give step by step solution.