Question

For L.P.P. maximize z = 4x₁ + 2x₂ subject to 3x₁ + 2x₂ ≥ 9, x₁ - x₂ ≤ 3, x₁ ≥ 0, x₂ ≥ 0 has ______.

Options

• infinite number of optimal solutions

• unbounded solution

• no solution

• one optimal solution

Answer 1

For L.P.P. maximize z = 4x₁ + 2x₂ subject to 3x₁ + 2x₂ ≥ 9, x₁ - x₂ ≤ 3, x₁ ≥ 0, x₂ ≥ 0 has unbounded solution.

Explanation:

We have, maximise z = 4x₁ + 2x₂ 

Subject to constracts, 3x₁ + 2x₂ ≥ 9, x₁ - x₂ ≤ 3, x₁ ≥ 0, x₂ ≥ 0

On taking given constraints as equation, we get the following graphs

Here, we get feasible region Is unbounded.