Question

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20) and (60, 0). If the objective function of an LPP is Z = 4x + 3y, then the maximum value is ______.

Options

• 200

• 300

• 240

• 120

Answer 1

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20) and (60, 0). If the objective function of an LPP is Z = 4x + 3y, then the maximum value is 300.

Explanation:

Substitute each given corner point (x, y) into the objective function Z = 4x + 3y:

Corner Point (x, y)	Value of Z = 4x + 3y	Result
(0, 0)	4(0) + 3(0)	0
(0, 40)	4(0) + 3(40)	120
(20, 40)	4(20) + 3(40) = 80 + 120	200
(60, 20)	4(60) + 3(20) = 240 + 60	300
(60, 0)	4(60) + 3(0)	240

Therefore, the maximum value is 300.