The Morton Supply Company produces clothing, footwear, and accessories for dancing and gymnastics.

They produce three models of pointe shoes used by ballerinas to balance on the tips of their toes. The shoes are produced from four materials: cardstock, satin, plain fabric, and leather. The number of square inches of each type of material used in each model of shoe, the amount of material available, and the profit/

model are shown below:

Material

(measured in square inches)

Model 1

Model 2

Model 3

Material Available Cardstock 12 10 14 1200 Satin 24 20 15 2000 Plain Fabric 45 40 30 7500 Leather 11 11 10 1000 Profit per model $50 $44 $40

a. Develop and solve an optimization model to find the number of each model to produce to maximize the total profit.

b. What constraints are binding? Interpret the slack values for the nonbinding constraints.

c. Clearly explain all the key information in the sensitivity report in language that the production manager would understand.