MHT CET · Maths · Linear Programming
The solution set of the inequalities \(4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0\) is represented by region
- A \(\mathrm{S}_2\) region
- B \(\mathrm{S}_1\) region
- C \(\mathrm{S}_3\) region
- D \(\mathrm{S}_4\) region
Answer & Solution
Correct Answer
(A) \(\mathrm{S}_2\) region
Step-by-step Solution
Detailed explanation
Take a test point \((4,10)\) that lies within the \(S_2\) region.
\(
\begin{aligned}
& \text { Since } 4(4)+3(10)=46 \leq 60,10 \geq 2(4)=8, \\
& 4 \geq 3,4 \geq 0,10 \geq 0
\end{aligned}
\)
\(\therefore\) The solution set is represented by \(\mathrm{S}_2\) region.
\(
\begin{aligned}
& \text { Since } 4(4)+3(10)=46 \leq 60,10 \geq 2(4)=8, \\
& 4 \geq 3,4 \geq 0,10 \geq 0
\end{aligned}
\)
\(\therefore\) The solution set is represented by \(\mathrm{S}_2\) region.
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