CUET · MATHS · PYQ PAPER 2025

Consider the following L.P.P.
Max. \(z=5 x+2 y\), subject to \(-2 x-3 y \leq-6, x-2 y \leq 2,3 x+2 y \leq 12,-3 x+2 y \leq 3\) and \(x, y \geq 0\) then

A Its feasible region is bounded and has 4 corner points
B Its feasible region is bounded and has 3 corner points
C Its feasible region is unbounded and has 4 corner points
D Its feasible region is unbounded and has 3 corner points

Verified Solution

Answer & Solution

Correct Answer

(A) Its feasible region is bounded and has 4 corner points

Step-by-step Solution

Detailed explanation

1. Rewrite constraints: \(L_1: 2x+3y \geq 6\) \(L_2: x-2y \leq 2\) \(L_3: 3x+2y \leq 12\) \(L_4: -3x+2y \leq 3\) \(x \geq 0, y \geq 0\) 2. Find intersection points of boundary lines: Point A: \(L_1 \cap L_4\) \(2x+3y=6\) \(-3x+2y=3\) \(x = \frac{3}{13}, y = \frac{24}{13}\) Point…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Consider the following L.P.P.Max. \(z=5 x+2 y\), subject to \(-2 x-3 y \leq-6, x-2 y \leq 2,3 x+2 y \leq 12,-3 x+2 y \leq 3\) and \(x, y \geq 0\) then

Step-by-step Solution

Consider the following L.P.P.
Max. \(z=5 x+2 y\), subject to \(-2 x-3 y \leq-6, x-2 y \leq 2,3 x+2 y \leq 12,-3 x+2 y \leq 3\) and \(x, y \geq 0\) then