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CUET · MATHS · PYQ PAPER 2025

Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize \(Z =5 x +2 y, Z =5 x +2 y, Z =5 x +2 y\)
subject to the following constraints
\(3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0\)
(A) The LPP has a unique optimal solution at \((2,0)\) only.
(B) The feasible region is bounded with corner points \((0,0),(2,0),(20 / 19,45 / 19)\) and \((0,3)\).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:

  1. A (A) and (D) only
  2. B (A), (B) and (C) only
  3. C (A), (C) and (D) only
  4. D (B) and (C) only
Verified Solution

Answer & Solution

Correct Answer

(D) (B) and (C) only

Step-by-step Solution

Detailed explanation

Vertices of feasible region: \((0,0)\) Line \(3x+5y=15\): Intersects \(x=0\) at \((0,3)\). Line \(5x+2y=10\): Intersects \(y=0\) at \((2,0)\). Intersection of \(3x+5y=15\) and \(5x+2y=10\): \(6x+10y=30\) \(25x+10y=50\) \(19x=20 \Rightarrow x=20/19\)…