MHT CET · Maths · Linear Programming

The shaded region in the following figure is the solution set of the inequations

A \(x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0\), \(x, y \geq 0\)
B \(x+2 y \leq 50,2 x+y \leq 100,2 x-y \leq 0\), \(x, y \geq 0\)
C \(x+2 y \geq 50,2 x+y \geq 100,2 x-y \leq 0\), \(x, y \geq 0\)
D \(x+2 y \leq 50,2 x+y \geq 100,2 x-y \leq 0\), \(x, y \geq 0\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0\), \(x, y \geq 0\)

Step-by-step Solution

Detailed explanation

Take a test point \((10,40)\) which lies within the feasible region.
Since \(10+2(40)=90 \geq 50\),
\(2(10)+40=60 \leq 100\),
\(2(10)-40=-20 \leq 0\)
\(\therefore \quad x+2 y \geq 50,2 x+y \leq 100,2 x-y \leq 0, x, y \geq 0\)

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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