MHT CET · Maths · Linear Programming

The shaded area in the figure below is the solution set for a certain linear programming problem, then the linear constraints are given by

A \(x \geqslant 1, y \leqslant 3, x-2 y \geqslant 2,6 x+7 \dot{y} \leqslant 42, x \geqslant 0, y \geqslant 0\)
B \(x \geqslant 1, y \leqslant 3, x-2 y \geqslant 2,6 x+7 y \geqslant 42, x \geqslant 0, y \geqslant 0\)
C \(x \leqslant 1, y \geqslant 3, x-2 y \leqslant 2,6 x+7 y \leqslant 42, x \geqslant 0, y \geqslant 0\)
D \(x \geqslant 1, y \leqslant 3, x-2 y \leqslant 2,6 x+7 y \leqslant 42, x \geqslant 0, y \geqslant 0\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(x \geqslant 1, y \leqslant 3, x-2 y \leqslant 2,6 x+7 y \leqslant 42, x \geqslant 0, y \geqslant 0\)

Step-by-step Solution

Detailed explanation

from the given lines we can conclude: the feasible region falls in:
\(\begin{aligned} & x \geqslant 1 \\ & y \leqslant 3 \\ & x-2 y \leqslant 2 \\ & 6 x+7 y \leqslant 42 \\ & x \geqslant 0, y \geqslant 0 \end{aligned}\)

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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