If feasible region is as shown in the figure, then related inequalities are

If feasible region is as shown in the figure, then related inequalities are
  1. $\begin{aligned} & 3 x+4 y \geq 12,4 x+7 y \leq 28, y \leq 1, x \geq 0, \\ & y \geq 0 \end{aligned}$
  2. $\begin{aligned} & 3 x+4 y \geq 12,4 x+7 y \leq 28, y \geq 1, x \geq 0, \\ & y \geq 0 \end{aligned}$
  3. $\begin{aligned} & 3 x+4 y \leq 12,4 x+7 y \leq 28, y \leq 1, x \geq 0, \\ & y \geq 0 \\ & 3 x+4 y \leq 12,4 x+7 y \geq 28, y \geq 1, x \geq 0, \\ & y \geq 0 \end{aligned}$
  4. $\begin{aligned} & 3 x+4 y \leq 12,4 x+7 y \geq 28, y \geq 1, x \geq 0, \\ & y \geq 0 \end{aligned}$

Solution

Shaded region lies on origin side of $4 x+7 y=28$ and above the line $y=1$, and on non-origin side of $3 x+4 y=12$. $\therefore \quad 3 x+4 y \geq 12,4 x+7 y \leq 28, y \geq 1, x \geq 0, y \geq 0$

Asked in: MHT CET 2023 (13 May Shift 1)

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