Question

Solve the following Linear Programming Problem graphically: Maximise Z = 3x + 4y subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.

Answer 1

Solution:

Given constraints are graph ,please see attachment

Points of intersection of three lines

x + y ≤ 4, x ≥ 0, y ≥ 0.

are A(0,0)

C(0,4)

B(4,0)

Now to Maximise Z = 3x + 4y

put the values of A ,B and C in the Z

$for \: A: \: Z = 3(0) + 4(0) = 0 \\ \\ \\ for \: B: \: Z = 3(4) + 4(0) = 12 \\ \\ for \: C: \: Z = 3(0) + 4(4) = 16$
So, Z is maximum at point C

when x =0 and y = 4

Hope it helps you.