CUET · MATHS · PYQ PAPER 2023
The programming problem
Max Z = 2x + 3y subject to the conditions \(0 \leq x \leq 3,0 \leq y \leq 4\) is:
- A not an LPP
- B an LPP, with unbounded feasible region and no solution
- C an LPP, and Max Z = 18 at x = 3, y = 4
- D an LPP, and Max Z = 12 at x = 0, y = 4
Answer & Solution
Correct Answer
(C) an LPP, and Max Z = 18 at x = 3, y = 4
Step-by-step Solution
Detailed explanation
Vertices: \( (0,0), (3,0), (0,4), (3,4) \) At \( (0,0): Z = 2(0) + 3(0) = 0 \) At \( (3,0): Z = 2(3) + 3(0) = 6 \) At \( (0,4): Z = 2(0) + 3(4) = 12 \) At \( (3,4): Z = 2(3) + 3(4) = 18 \) Max Z = 18 at x = 3, y = 4
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