Question

Solve the following linear programming problem graphically:

Maximise Z = 2x +3y
subject to the constraints:

x +y ≤ 6
x ≥ 2
y ≤ 3
x, y ≥ 0

Answer 1

Constraints:

x +y ≤ 6
x ≥ 2
y ≤ 3
x, y ≥ 0

Let x + y = 6

x	0	6	1
y	6	0	5

Corner points	z = 2x + 3y
A (2, 0)	2 × 2 + 3 × 0 = 4
B (6, 0)	2 × 6 + 3 × 0 = 12
C (3, 3)	2 × 3 + 3 × 3 = 15
D (2, 4)	2 × 2 + 3 × 4 = 16

Maximum value of Z is 16 at D (2, 4)