CUET · MATHS · PYQ PAPER 2025
For the linear programming problem (LPP),
Maximize \(Z=4 x+y\)
Subject to:
\(x+y \leq 5\)
\(3 x+y \leq 9\)
\(x, y \geq 0\)
Which of the following are NOT true?
(A) The given LPP has unbounded feasible region.
(B) The corner points of the feasible region are \((0,0),(0,5),(3,2)\) and \((3,0)\).
(C) The optimal value of the objective function is 12.
(D) The given LPP has a unique optimal solution.
Choose the correct answer from the options given below:
- A (A), (B) and (D) only
- B (A), (B) and (C) only
- C (A) and (B) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(C) (A) and (B) only
Step-by-step Solution
Detailed explanation
Vertices of feasible region: \((0,0)\) \(x=0, x+y=5 \implies (0,5)\) \(y=0, 3x+y=9 \implies (3,0)\) \(x+y=5, 3x+y=9 \implies 2x=4, x=2, y=3 \implies (2,3)\) Corner points: \((0,0), (0,5), (3,0), (2,3)\) Evaluate \(Z=4x+y\): \(Z(0,0)=0\) \(Z(0,5)=5\) \(Z(3,0)=12\) \(Z(2,3)=11\)…
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