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 tops 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 the 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 1,200 Satin 54 20 15 2,000 Plain Fabric 40 40 30 7,500 Leather 11 11 10 1,000 Profit Per Model $50 $44 $40 Mathematically formulate a linear optimization model and solve the problem.