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

Please help answer the following:

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

b. Mathematically formulate a linear optimization model. c. Implement the linear optimization model that you developed on a spreadsheet and use Solver to find an optimal solution. Interpret the Solver Answer Report and identify the binding constraints

Answer 1

A)

The decision variable are:

Number of Model 1 pointe shoes

Number of Model 2 pointe shoes

Number of Model 3 pointe shoes

The objective function is the profit maximization where the profits for model 1, 2 and 3 are $ 50, $ 44, $ 40 respectively.

There are 4 constraints involved:

Maximum 1200 square inches of Cardstock is available and per model usage is 12, 10 and 14 square inches respectively in one product

Maximum 2000 square inches of Satin is available and per model usage is 24, 20 and 15 square inches respectively in one product

Maximum 7500 square inches of Plain Fabric is available and per model usage is 40, 40 and 30 square inches respectively in one product

Maximum 1000 square inches of Leather is available and per model usage is 11, 11 and 10 square inches respectively in one product

B)

Let X be the Number of Model 1 pointe shoes

Let Y be the Number of Model 2 pointe shoes

Let Z be the Number of Model 3 pointe shoes

Objective Function:

Maximize: 50X + 44 Y + 40 Z

Subject to constraints:

12X + 10Y + 14Z <=1200

24X + 20Y + 15Z <= 2000

40X + 40Y + 30Z <= 7500

11X + 11Y + 10Z <= 1000

X,Y,Z >= 0

C) Putting the data into the spread sheet and running the solver, we get:

The binding constraints are:

Therefore,

The Maximum profit can be $ 4400

The Maximum Number of Model 1 pointe shoes that can be produced are 67 approximately

The Maximum Number of Model 3 pointe shoes that can be produced are 27 approximately

Model 2 pointe shoes must not be produced in order to keep the profits maximum