Question

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.

X1 = number of product 1 produced in each batch
X2 = number of product 2 produced in each batch

MAX: 150 X1 + 250 X2
Subject to: 2X1 + 5 X2 ≤ 200
3X1 + 7 X2 ≤ 175
  X1, X2 ≥ 0

How many units of resource two (the second constraint) are unutilized if the company produces 10 units of product 1 and 5 units of product 2?
a. 110
b. 150
c. 155
d. 100

Answer 1

option a

second constraint = 3x1 + 7x2 ≤ 175

if x1 = 10 and x2= 5 , putting these value in the equation

3(10) + 7*5= 30 + 35 = 65 units used

units of resource 2 ( full amount )= 175

units used = 65

so unused resource = 175 - 65

= 110