Question

The corner points for the bounded feasible region determined by the system of inequalities: 5x + 2y < 40 x + 3Y < 21 x,y > 0 are O = (0, 0), A = (0, 7), B = (6, 5) and C = (8, 0). Find the optimal solution for the objective profit function: maximize P = 10x + 5y.

Answer 1

Explanation:

Given

5x+2y<40

x+3y<21

These two lines intersect at (6,5)

we have to maximize 10x+5y

Four corner points are

(0,0)
`\Rightarrow`10(0)+5(0)=0

(0,7)
`\Rightarrow`10(0)+5(7)=35

(6,5)
`\Rightarrow`10(6)+5(5)=85

(8,0)
`\Rightarrow`10(8)+5(0)=80

At x=6 and y=5 optimal solution is obtained.