CUET · MATHS · PYQ PAPER 2023

Corner points of the feasible region for a linear programming problem are \((0,2),(3,0),(6,0)\) and \((0,5)\). Let \(F=4 x+6 y\) be the objective function. The minimum value of \(F\) occurs at:

A \((0,2)\) only
B \((3,0)\) only
C any point on the line joining the points \((0,2)\) and \((3,0)\) only
D the mid point of the line segment joining the points \((0,2)\) and \((3,0)\) only

Verified Solution

Answer & Solution

Correct Answer

(C) any point on the line joining the points \((0,2)\) and \((3,0)\) only

Step-by-step Solution

Detailed explanation

\(F(0,2) = 4(0) + 6(2) = 12\) \(F(3,0) = 4(3) + 6(0) = 12\) \(F(6,0) = 4(6) + 6(0) = 24\) \(F(0,5) = 4(0) + 6(5) = 30\) The minimum value of \(F\) is 12, which occurs at \((0,2)\) and \((3,0)\). The minimum value occurs at any point on the line joining the points \((0,2)\) and…

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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