CUET · MATHS · PYQ PAPER 2023

If the objective function for an L.P.P. is \(z=3 x-4 y\) and the corner points for the bounded feasible region are \((0,0),(5,0),(6,5),(6,8),(4,10)\) and \((0,8)\), then the minimum value of \(z\) occurs at :

A (0,0)
B (6,5)
C (0,8)
D (4,10)

Verified Solution

Answer & Solution

Correct Answer

(C) (0,8)

Step-by-step Solution

Detailed explanation

\(z(0,0) = 3(0) - 4(0) = 0\) \(z(5,0) = 3(5) - 4(0) = 15\) \(z(6,5) = 3(6) - 4(5) = -2\) \(z(6,8) = 3(6) - 4(8) = -14\) \(z(4,10) = 3(4) - 4(10) = -28\) \(z(0,8) = 3(0) - 4(8) = -32\) Minimum value is \(-32\) at \((0,8)\).

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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From CUET

Match List-I with List-II

List-I	List-II
(A) Catalysts alter the rate of reaction	(I) cannot be fraction or zero
(B) Molecularity	(II) by lowering the activation energy
(C) Second half life of a first order reaction	(III) is the same as the first
(D) \(e^{-E_a / R T}\)	(IV) refers to the fraction of molecules with energy equal to or greater than activation energy

Choose the correct answer from the options given below:

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