A company makes two types of products, A and B. These products are produced during a 40-hour work week and then shipped out at the end of the week. They require 20 and 5 kg of raw material per kg of product, respectively, and the company has access to 9500 kg of raw material per week. Only one product can be created at a time with production times for each of 0.04 and 0.12 hr, respectively. The plant can only store 550 kg of total product per week. Finally, the company makes profits of $45 and $20 on each unit of A and B, respectively. Each unit of product is equivalent to a kg.

(a) Set up the linear programming problem to maximize profit.

(b) Solve the linear programming problem graphically.

(c) Solve the linear programming problem with the simplex method.

(d) Solve the problem with a software package.

(e) Evaluate which of the following options will raise profits the most: increasing raw material, storage, or production time.