Question: A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table.

Product Material 1 (lbs.) Material 2 (lbs.) Labor (hours)

A 3 2 4

B 1 4 2

C 5 none 3.5

Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for $67 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. Also, there is a weekly demand of 10 units of product C each week. Use linear programming to formulate the problem.