Q76 / 150 · MHT CET 2021 (20 Sep Shift 1) · Mathematics

The shaded part of the given figure indicates the feasible region. Then the constraints are Figure

  • Correct answer
    A
    $\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}-\mathrm{y} \geq 0 ; \mathrm{x} \leq 5 ; \mathrm{y} \leq 3$
  • B
    $x, y \geq 0 ; x-y \geq 0 ; x \leq 5 ; y \geq 3$
  • C
    $\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}+\mathrm{y} \geq 0 ; \mathrm{x} \geq 5 ; \mathrm{y} \leq 3$
  • D
    $x, y \geq 0 ; x-y \geq 0 ; x \geq 5 ; y \leq 3$

Solution

Here equation of line $\mathrm{OC}$ is $\mathrm{y}=\mathrm{x}$ i.e. $\mathrm{x}-\mathrm{y}=0$ and equation of line $\mathrm{AB}$ is $\mathrm{x}=5$ i.e. $\mathrm{x}-5=0$ Equation of line $\mathrm{BC}$ is $\mathrm{y}=3$ i.e. $\mathrm{y}-3=0$ Hence constraints for the shaded region are $x, y \geq 0, x-5 \leq 0, x$ $$ \begin{aligned} & -y \geq 0, y-\leq 0 \\ & \text { i.e. } x, y \geq 0, x \leq 5, x-y \geq 0, y \leq 3 \end{aligned} $$

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

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