MHT CET · Maths · Linear Programming

If feasible region is as shown in the figure, then the related inequalities are

A \(3 x+4 y \geq 12, y-x \geq 0, y \leq 3, x, y \geq 0\)
B \(3 x+4 y \leq 12, y-x \leq 0, y \geq 3, x, y \geq 0\)
C \(3 x+4 y \leq 12, y-x \geq 0, y \leq 3, x, y \geq 0\)
D \(3 x+4 y \geq 12, y-x \leq 0, y \geq 3, x, y \geq 0\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(3 x+4 y \geq 12, y-x \geq 0, y \leq 3, x, y \geq 0\)

Step-by-step Solution

Detailed explanation

The shaded region lies:
on non-origin side of line \(3 x+4 y=12\) i.e., \(3 x+4 y \geq 12\),
on the side of the line \(y-x=0\), where \(y \geq x\) i.e., \(y-x \geq 0\),
on origin side of line \(y=3\)
i.e., \(y \leq 3\),
and in first quadrant
i.e., \(x \geq 0, y \geq 0\).

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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