CUET · MATHS · PYQ PAPER 2023

The linear programming problem: Minimise \(Z=3 x+2 y\)
Subject to constraints: \(x+y \geq 8, \quad 3 x+5 y \leq 15, \quad x \geq 0, y \geq 0\) has

A Feasible solutions
B no feasible solutions
C bounded region
D feasible solution at \(x=0, y=0\)

Verified Solution

Answer & Solution

Correct Answer

(B) no feasible solutions

Step-by-step Solution

Detailed explanation

Consider region \((x,y)\) satisfying \(3x+5y \le 15, x \ge 0, y \ge 0\). Vertices: \((0,0), (5,0), (0,3)\). Maximum value of \(x+y\) in this region: \(\max(0+0, 5+0, 0+3) = 5\). Thus, any point satisfying \(3x+5y \le 15, x \ge 0, y \ge 0\) must also satisfy \(x+y \le 5\). The…

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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The linear programming problem: Minimise \(Z=3 x+2 y\)Subject to constraints: \(x+y \geq 8, \quad 3 x+5 y \leq 15, \quad x \geq 0, y \geq 0\) has

Step-by-step Solution

The linear programming problem: Minimise \(Z=3 x+2 y\)
Subject to constraints: \(x+y \geq 8, \quad 3 x+5 y \leq 15, \quad x \geq 0, y \geq 0\) has