Question

Solve the LPP 

Maximize z = 30x + 25y

Subjected to 3x + 3y ≤ 18 and 3x + 2y ≤ 15

x ≥ 0, y ≥ 0.

Answer 1

The given inequalities can be written in the form of equation as 

3x + 3y = 18 ...(i)

and 3x + 2y = 15 ...(ii)

First we draw the line of above equation. 

These lines intersect at P(3,3)

The feasible region is OCPBO which is bounded

The vertices of the fesible region are:

O(0,0), C(5,0), P(3,3) & B(0,6)

Given, Z = 30x + 25y

At O(0,0), Z = 0

At C(5,0), Z = 150

At P(3,3), Z = 165

At B(0,6), Z = 150

So, the maximum profit is Rs. 165