Question

Solve the following L.P.P. using graphical methods:

Max Z = 6x₁ + 8x₂

Subject to

5x₁ + 10x₂ ≤ 60

4x₁ + 4x₂ ≤ 40

x₁, x₂ ≥ 0

Answer 1

Convert all the equalities of the constraint into equations, we have

5x₁ + 10x₂ = 60 

4x₁ + 4x₂ = 40

5x₁ + 10x₂ = 60 passes through (0, 6) and (12, 0)

4x₁ + 4x₂ = 40 passes through (0, 10) and (10, 0)

Plot the above equations on graph, we have.

Now the coordinates of points ABCD are A(0, 10), B(1, 5), C(4, 2), D(12, 0)

Corner Points	Coordinate	Value of Z
A	(0, 10)	20
B	(1, 5)	13
C	(4, 2)	16
D	(12, 0)	36

Hence, minimum value occurs at point B(1, 5).

Therefore, optimum solution is given by x₁ = 1, x₂ = 5 and min Z = 13.