Question

Solve the following L.P.P. by graphical method:

Max Z = 3x₁ + 2x₂

S.T. 

x₁ – x₂ ≥ 1

x₁ + x₂ ≥ 3

x₁, x₂ ≥ 0

Answer 1

Convert the inequality constraints into equations.

We have

x₁ – x₂ = 1

x₁ + x₂ = 3

Now x₁ – x₂ = 1 passes through (0, –1) and (1, 0)

x₁ + x₂ = 3 passes through (0, 3) and (3, 0)

Plot above equations on graph, we have

Here the solution space is unbounded. The value of objective function at the vertices A and B are Z(A) = 6, Z(B) = 6. But there exists points in the convex region for which the value of the objective function is more than 8. In fact, the maximum value of Z occurs at infinity.

Hence, the problem has an unbounded solution.