The Great Threads Company is capable of manufacturing shirts, shorts, pants, skirts, and jackets. Each type of clothing requires Great Threads to acquire the appropriate type of machinery. The machinery needed to manufacture each type of clothing must be rented at the weekly rates shown in the table below. This table also lists the amounts of cloth and labor required per unit of clothing, as well as the net profit for each type of clothing. There are 4000 labor hours and 4500 square yards (sq yd) of cloth available each week. The company wants to find a solution that maximizes its weekly profit. Formulate this problem as a mixed-integer programming model.

 

 

Rental Cost Labor Hours Cloth (sq yd) Profit Shirts $1500 2.0 3.0 $35 Shorts $1200 1.0 2.5 $40 Pants $1600 6.0 4.0 $65 Skirts $1500 4.0 4.5 $70 Jackets $1600 8.0 5.5 $110