Question

A furniture company manufactures desks and chairs. The sawing department cuts the

lumber for both products, which is then sent to separate assembly departments. Assembled

items are sent to the painting department for finishing. The daily capacity of the sawing

department is 200 chairs or 80 desks. The chair assembly department can produce 120 chairs

daily, and the desk assembly department 60 desks daily. The paint department has a daily

capacity of either 150 chairs or 110 desks. Given that the profit per chair is $50 and that of a

desk is $100, determine the optimal production mix for the company.​

Answer 1

Given:

The daily capacity of the sawing  department is 200 chairs or 80 desks.

The chair assembly department can produce 120 chairs  daily, and the desk assembly department 60 desks daily.

The paint department has a daily  capacity of either 150 chairs or 110 desks.

The profit per chair is $50 and that of a  desk is $100

To find:

Determine the optimal production mix for the company.​

Solution:

Max Z = 50x + 100y

Subject to

x + 2.5y ≤ 200          Sawing

11x + 15y ≤ 1650        Paint

x ≤ 120                       Chair assembly

y ≤ 60                        Desk assembly

The value of the objective function at each of these extreme points is as follows:

Extreme Point  Coordinates          Objective function value

(x,y)                                                        z=50x+100y                

A(120,0)                                                 50(120)+100(0)=6000

B(120,22)                                               50(120)+100(22)=8200

C(90,44)                                                 50(90)+100(44)=8900

D(50,60)                                                 50(50)+100(60)=8500

E(0,60)                                                    50(0)+100(60)=6000

The maximum value of the objective function z=8900 occurs at the extreme point (90,44).

Number of chair = 90

Number of desk = 44

Maximum profit = $8900