Question

A print shop at a community college in Cupertino, California, employs two different contractors to maintain its copying machines. The print shop needs to have 12 IBM, 18 Xerox, and 20 Canon copying machines serviced. Contractor A can repair 2 IBM, 1 Xerox, and 2 Canon machines at a cost of $800 per month, while Contractor B can repair 1 IBM, 3 Xerox, and 2 Canon machines at a cost of $1000 per month. How many months should each of the two contractors be employed to minimize the cost?

Answer 1

Algebraic formulation

Let

A = No. of months of employment of Contractor-A
B = No. of months of employment of Contractor-B

Min Z = 800 A + 1000 B

Subject to,

2 A + 1 B >= 12 (IBM)

1 A + 3 B >= 18 (Xerox)

2 A + 2 B >= 20 (Canon)

A, B >= 0

LINDO Code

Min 800 A + 1000 B
s.t.
2 A + 1 B > 12
1 A + 3 B > 18
2 A + 2 B > 20
end

Solution

So,

Contractor-A and B should be employed for 6 and 4 months respectively.