Question

The maximum value of z = 4x + 2y subject to the constraints $2x+3y\le 18,x+y\le 10,x\ge 0,y\ge 0,$ is ____________.

Answer 1

for z = 4x + 2y
S.t 2x + 3y ≤ 18
x + y ≤ 10
The feasible region of the system of inequalities given in the constraints,
we convert inequalities to equalities
2x + 3y = 18, x + y = 10, x = 0, y = 0
Here feasible region is given by shaded region A, B, C, D

Points	Value of z = 4x + 2y
A (0, 6)	z = 4(0) + 2(6) = 12
B (9, 0)	z = 4(9) + 2(0) = 36
C (10, 0)	z = 4(10) + 2(0) = 40
D (0, 10)	z = 4(0) + 2(10) = 20

∴ Maximum value of z = 4x + 2y is 36