Question

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is z = 4x + 3y.
Compare the quantity in Column A and Column B
Column A Column B
Maximum of z 325
(a) The quantity in Column A is greater
(b) The quantity in Column B is greater
(c) The two quantities are equal
(d) The relationship can not determined on the basis of information supplied.

Answer 1

Points	Value of z
(0, 0)	0
(0, 4, 0)	120
(20, 40)	200
(60, 20)	300
(60, 0)	240

Given, z = 4x + 3y
Given feasible points are;
(0, 0), (0, 40), (20, 40), (60, 20), (60, 0)
z(0, 0) = 4(0) + 3(0) = 0
z(0, 40) = 4(0) + 3(40) = 120
z(20, 40) = 4(20) + 3(40) = 80 + 120 = 200
z(60, 20) = 4(60) + 3(20)
= 240 + 60
= 300
z(60, 0) = 4(60) + 3(0)
z(60, 0) = 240
∴ max z = 300
i.e. column A is 300 and column B is 325
∴ The quantity of B is greater than A.
Hence, the correct answer is option B.