The GATE Grind

GATE 2018 ME (ME2) – Question 45

Operations Research · Linear programming and the simplex method · 2 marks · Multiple choice

Maximize $z=x_1-x_2$ subject to $x_1+x_2\le10$, $x_1\ge0$, $x_2\ge0$, $x_2\le5$. The problem has ______.

  1. no solution
  2. one solution
  3. two solutions
  4. more than two solutions

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) one solution

Explanation

Since $x_1\le10-x_2$, $z=x_1-x_2\le10-2x_2\le10$. Equality requires $x_2=0$ and $x_1=10$. This feasible point is unique, so there is **one optimal solution, B**.