Question

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	1,200
Satin	24	20	15	2,000
Plain fabric	40	40	30	7,500
Leather	11	11	10	1,000
Profit per model	$50	$44	$40

1. Identify the decision variables, objective function, and constraints in simple verbal statements.

2. Mathematically formulate a linear optimization model.

3. Please show Step 2 in Excel

Answer 1

Decision variables :Number of units to produce of each model type

Objective function:Maximize total profit

Max z=50x1+44x2+40x3 ; where x1,x2 and x3 are number of model 1,2 and 3 types.

Constraints :The maximum available cardstock material is 1200 ,Satin is 2000 ,Plain fabric is 7500 and Leather is 1000

Using excel solver,we find the optimal solution that maximizes total profit.

Total profit=SUMPRODUCT(B13:D13,B10:D10)=$ 4400

In excel,

B19=SUMPRODUCT(B13:D13,B4:D4)

B20=SUMPRODUCT(B13:D13,B5:D5)

B21=SUMPRODUCT(B13:D13,B6:D6)

B22=SUMPRODUCT(B13:D13,B7:D7)

The optimal solution is :

Number of model 1 shoes=66.667=67

Number of model 2 shoes=0

Number of model 3 shoes=26.667=27