The maximum value of z = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60 x, y ≥ 0, is ____________.

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Solution

For z = 3x + 4y
s.t x + y ≤ 40
x + 2y ≤ 60, x, y ≥ 0
The equality constraints corresponding to give inequalities are x + y = 40, x + 2y = 60, x = 0, y = 0

The feasible region is given by OABC

Points Value of z = 3x + 4y

O(0, 0) z = 3(0) + 4(0) = 0

A (40, 0) z = 3(40) + 4(0) = 120

B (20, 20) z = 3(20) + 4(20) = 140

C(0, 30) z = 3(0) + 4(30) = 120

∴ Maximum value of z = 3x + 4y = 140

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