CUET · MATHS · PYQ PAPER 2023
Consider \(Z = x + y\) subject to the constraints \(2x + y \le 3, 2x - y \ge 0, x \ge 0, y \ge 0\). The maximum value of Z is:
- A \(\frac{3}{2}\)
- B \(\frac{5}{2}\)
- C \(\frac{7}{4}\)
- D \(\frac{9}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{4}\)
Step-by-step Solution
Detailed explanation
Vertices: \((0,0)\) \(y=0, 2x+y=3 \implies (3/2, 0)\) \(y=2x, 2x+y=3 \implies 2x+2x=3 \implies x=3/4 \implies y=3/2 \implies (3/4, 3/2)\) Evaluate \(Z=x+y\): \(Z(0,0) = 0+0 = 0\) \(Z(3/2,0) = 3/2+0 = 3/2\) \(Z(3/4,3/2) = 3/4+3/2 = 3/4+6/4 = 9/4\) Maximum value of Z is…
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