Sample linear programming problems to calculate max profit, Operation Research

The following linear programming is written to plan the production of two products. And the company wants to maximize profits.

x1 = number of product 1 produced in each batch

x2 = number of product 2 produced in each batch

Max subject to"

150x1+250x2

2x1+ 5x2 <= 200

3x1 + 7x2 <= 175

X1, x2 >= 0

How much profit is earned per each unit of product 2 produced?

a.     150

b.     175

c.      200

d.     250

 Given that

  Max Z = 150 x1 + 250 x2

 Subject to

2x1 + 5x2 <= 200

3x1 + 7x2 <= 175

And x1, x2 >= 0                  

From constraints

  2x1 + 5x2 = 200..............................  (A)

3x1 + 7x2 = 175 ...................................(B)

Or

6x1 + 15x2 = 600

6x1 + 14x2 = 350

Subtracting

X2 = 250

 Put value of x2 in equation (A), we get

2x1 = 200 - 1250 = - 1050

ð X1 = -525 which is meaning less because x1 >= 0, x2>= 0

Thus x1 = 0 and x2 = 250 .

To maximize profit , company should produce 250 units of product 2.

(d) is right answer

10.   Given  that x1 unit of resources 1, and x2 unit of resources 2.

 According to the problem

4x1 + 3x2 <= 150

Thus (b) is right answer 

Posted Date: 7/11/2012 4:33:44 AM | Location : United States







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