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

The shaded part of the given figure indicates the feasible region. Then the constraints are
  1. $\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}-\mathrm{y} \geq 0 ; \mathrm{x} \leq 5 ; \mathrm{y} \leq 3$
  2. $x, y \geq 0 ; x-y \geq 0 ; x \leq 5 ; y \geq 3$
  3. $\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}+\mathrm{y} \geq 0 ; \mathrm{x} \geq 5 ; \mathrm{y} \leq 3$
  4. $x, y \geq 0 ; x-y \geq 0 ; x \geq 5 ; y \leq 3$

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 $x, y \geq 0, x-5 \leq 0, x$ $\begin{aligned} & -y \geq 0, y-\leq 0 \\ & \text { i.e. } x, y \geq 0, x \leq 5, x-y \geq 0, y \leq 3 \end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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