Problem #$1(10$ pts$).$

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:

$\backslash$table$[[\backslash$table$[[$Material$],[($measured$],[$in square inches$)]],\backslash$table$[[$Model$],[1]],\backslash$table$[[$Model$],[2]],\backslash$table$[[$Model$],[3]],\backslash$table$[[$Material$],[$Available$]]],[$Cardstock$,12,10,14,1200],[$Satin$,24,20,15,2000],[$Plain Fabric,$40,40,30,7500],[$Leather$,11,11,10,1000],[$Profit per model,$$50,$$$44,$$$40,]]$

a$)$ Identify the decision variables, objective function, and constraints in simple verbal statements.

b$)$ Mathematically formulate a linear optimization model.