Question

Maximised value of z in z = 3x + 4y, subject to constraints : x + y ≤ 4, x ≥ 0. y ≥ 0

विकल्प

• 16

• 18

• 14

• 12

Answer 1

16

Explanation:

Objective function is z = 3x + 4y constrains are, x + y ≤ 4, x  ≥ 0, y  ≥ 0 consider the line x + y = 4

It passes through the points (4, 0) and (0, 4) putting x = 0, y = 0 in x + y ≤ 4, we get 0 ≤ 4 which is true.

Therefore origin lies in the region x + y ≤ 4

x ≥ 0 is the region to the right of y-axis and y ≥ 0 is the region on and above x-axis.

The feasible region in ΔOAB is

At (4, 0)	z = 3x + 4y = 3 × 4 + 0 = 12
At (0, 4)	z = 3x + 4y = 0 + 4 × 4 = 16
At (0, 0)	z = 0

∴ Maximum value of z = 16.