Q68 / 150 · MHT CET 2024 (02 May Shift 2) · Mathematics

The shaded region in the following figure is the solution set of the inequations Figure

  • Correct answer
    A
    $x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0$, $x, y \geq 0$
  • B
    $x+2 y \leq 50,2 x+y \leq 100,2 x-y \leq 0$, $x, y \geq 0$
  • C
    $x+2 y \geq 50,2 x+y \geq 100,2 x-y \leq 0$, $x, y \geq 0$
  • D
    $x+2 y \leq 50,2 x+y \geq 100,2 x-y \leq 0$, $x, y \geq 0$

Solution

Take a test point $(10,40)$ which lies within the feasible region. Since $10+2(40)=90 \geq 50$, $2(10)+40=60 \leq 100$, $2(10)-40=-20 \leq 0$ $\therefore \quad x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0, x, y \geq 0$

Hence, the correct answer is option: 'A'.

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