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