CUET · MATHS · PYQ PAPER 2023
The point at which the maximum value of \(x+y\), subject to constraints \(x+2 y \leq 70,2 x+y \leq 95, x \geq 0, y \geq 0\) is obtained, is :
- A (30,25)
- B (20,35)
- C (35,20)
- D (40,15)
Answer & Solution
Correct Answer
(D) (40,15)
Step-by-step Solution
Detailed explanation
\(x+2y=70\) \(2x+y=95\) \(2(70-2y)+y=95\) \(140-4y+y=95\) \(3y=45 \Rightarrow y=15\) \(x=70-2(15)=40\) Vertices and objective values \(x+y\): \((0,0) \rightarrow 0\) \((0,35) \rightarrow 35\) \((47.5,0) \rightarrow 47.5\) \((40,15) \rightarrow 40+15=55\) \((40,15)\)
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