CUET · MATHS · PYQ PAPER 2023

Objective function \(z=200 x+500 y\), subject to the constraints
\(x+2 y \geq 10, \quad 3 x+4 y \leq 24, \quad x \geq 0, \quad y \geq 0\),
the minimum value of \(z\) is :

A 2500
B 3000
C \(0\)
D 2300

Verified Solution

Answer & Solution

Correct Answer

(D) 2300

Step-by-step Solution

Detailed explanation

Vertices of the feasible region: \(x=0, x+2y=10 \Rightarrow (0,5)\) \(x=0, 3x+4y=24 \Rightarrow (0,6)\) \(x+2y=10, 3x+4y=24 \Rightarrow (4,3)\) Evaluate \(z=200 x+500 y\) at vertices: \(z(0,5) = 200(0)+500(5) = 2500\) \(z(0,6) = 200(0)+500(6) = 3000\)…

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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	Size	Mean	Standard Deviation
Sample 1	4	40	8
Sample 2	5	50	10

Objective function \(z=200 x+500 y\), subject to the constraints\(x+2 y \geq 10, \quad 3 x+4 y \leq 24, \quad x \geq 0, \quad y \geq 0\),the minimum value of \(z\) is :

Step-by-step Solution

Objective function \(z=200 x+500 y\), subject to the constraints
\(x+2 y \geq 10, \quad 3 x+4 y \leq 24, \quad x \geq 0, \quad y \geq 0\),
the minimum value of \(z\) is :