Question

A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A desk contributes $400 to profit, and a chair contributes $250. • Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 2000 units of wood available.

a. What are the decision Variables?

B. what is the objective function?

C. What are the constraints?

D. Use Solver to maximize the company's Profit

Answer 1

1. The decision variables are X and Y

X= Number of Desks

Y= number of chairs

2. The objective function is :

Maximize Z=400X+ 250Y

3. The constraints are as follows:

4X+3Y<or=2000

2X<or=Y

X>or=0

y>or=0

4. Company’s profit is maximized when

200 desks and 400 chairs are sold(Note below)

NOTE:

Let X= Number of Desks

Let Y= number of chairs

Each unit of desk requires 4 units of wood

Each unit of chair requires 3 units of wood

Therefore 4X+3Y<or=2000

Number of chairs produced should be at least twice the number of desks

2X<or=Y

X>or=0

Y>or=0

Solving the above equation we get:

4(Y/2)+3Y=2000

Therefore Y=400

X=200(Y/2)