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Question: Answered & Verified by Expert
The shaded region in the following figure represents the solution set for a certain linear programming problem. Then linear constraints for this region are given by

MathematicsLinear ProgrammingMHT CETMHT CET 2023 (14 May Shift 2)
Options:
  • A $\begin{aligned} 2 x+3 y \geq 6,-x+2 y & \geq 2,3 x+6 y \leq 18, \\ x-3 y & \geq 3, x \geq 0, y \geq 0\end{aligned}$
  • B $\begin{aligned} 2 x+3 y \geq 6,-x+2 y & \leq 2, x-3 y \leq 3 \\ x+2 y & \geq 18, x \geq 0, y \geq 0\end{aligned}$
  • C $\begin{aligned} 2 x+3 y \leq 6,-x+2 y & \geq 2,3 x+6 y \leq 18 \\ x-3 y & \leq 3, x \geq 0, y \geq 0\end{aligned}$
  • D $\begin{aligned} 2 x+3 y \geq 6,3 x+6 y & \leq 18, x-3 y \leq 3 \\ -x+2 y & \leq 2, x \geq 0, y \geq 0\end{aligned}$
Solution:
1018 Upvotes Verified Answer
The correct answer is: $\begin{aligned} 2 x+3 y \geq 6,3 x+6 y & \leq 18, x-3 y \leq 3 \\ -x+2 y & \leq 2, x \geq 0, y \geq 0\end{aligned}$
Shaded region lies on origin side of $3 x+6 y=18, x-3 y=3,-x+2 y=2$ and on non-origin side of $2 x+3 y=6$.
$\begin{aligned}
\therefore \quad & 2 x+3 y \geq 6,3 x+6 y \leq 18, x-3 y \leq 3, \\
& -x+2 y \leq 2, x \geq 0, y \geq 0
\end{aligned}$

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