Problem 6. (20 pt.) The Lovely Apparel Company produces shirts, shorts, pants, skirts, and jackets. The company needs to have the appropriate type of equipment available for each type of clothing item. The equipment (with unlimited weekly production capacity) required to produce each type of clothing item has to be rented at the weekly rates shown in the following table. This table also shows the amounts of cloth and labor needed per unit of clothing, as well as the sales price and the unit variable cost for each type of clothing item. Rental Cost Labor Hours Cloth (sq yd) Sales Price Unit Variable Cost Shirts $1500 $35 $20 Shorts $1200 $40 $10 Pants $1600 Skirts $1500 4.0 4.5 $30 Jackets $1600 $110 $35 There are 5000 labor hours and 5000 square yards (sq yd) of cloth available in a given week. The company needs to find an optimal production plan that maximizes its weekly profit. 2.0 1.0 3.0 2.5 4.0 6.0 $25 $65 $70 8.0 5.5 a. Formulate an optimization model for this problem algebraically. b. Formulate and solve an optimization model for this problem on a spreadsheet