CUET · MATHS · PYQ PAPER 2025
The minimum value of \(Z = 2x + y\) subjected to \(x + y ≥ 10, 2x + 3y ≤ 26, x, y ≥ 0\) is
- A 14
- B 20
- C 26
- D 30
Answer & Solution
Correct Answer
(A) 14
Step-by-step Solution
Detailed explanation
Vertices of the feasible region: \( P_1 = (10, 0) \) \( P_2 = (13, 0) \) \( P_3 = (4, 6) \) Evaluate \( Z = 2x + y \) at each vertex: \( Z(P_1) = 2(10) + 0 = 20 \) \( Z(P_2) = 2(13) + 0 = 26 \) \( Z(P_3) = 2(4) + 6 = 8 + 6 = 14 \) Minimum value of \( Z = 14 \)
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