MHT CET · Maths · Linear Programming
The shaded part of the given figure indicates the feasible region. Then the constraints are
- 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 \(x, y \geq 0 ; x-y \geq 0 ; x \geq 5 ; y \leq 3\)
Answer & Solution
Correct Answer
(A) \(\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}-\mathrm{y} \geq 0 ; \mathrm{x} \leq 5 ; \mathrm{y} \leq 3\)
Step-by-step Solution
Detailed explanation
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 \(x, y \geq 0, x-5 \leq 0, x\)
\(
\begin{aligned}
& -y \geq 0, y-\leq 0 \\
& \text { i.e. } x, y \geq 0, x \leq 5, x-y \geq 0, y \leq 3
\end{aligned}
\)
Equation of line \(\mathrm{BC}\) is \(\mathrm{y}=3\) i.e. \(\mathrm{y}-3=0\)
Hence constraints for the shaded region are \(x, y \geq 0, x-5 \leq 0, x\)
\(
\begin{aligned}
& -y \geq 0, y-\leq 0 \\
& \text { i.e. } x, y \geq 0, x \leq 5, x-y \geq 0, y \leq 3
\end{aligned}
\)
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