MHT CET · Maths · Linear Programming

The graphical solution set for the system of inequations
\(x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0,\)
\(y \geq 0\) is given by

A Fig.2
B Fig.4
C Fig.1
D Fig.1

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Answer & Solution

Correct Answer

(D) Fig.1

Step-by-step Solution

Detailed explanation

Feasible region lies on origin side of \(x-2 y=2\), \(4 x+5 y=20\) and on non-origin side of \(5 x+2 y=10\), in \(1^{\text {st }}\) quadrant.

Fig.3

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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The graphical solution set for the system of inequations\(x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0,\)\(y \geq 0\) is given by

Step-by-step Solution

The graphical solution set for the system of inequations
\(x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0,\)
\(y \geq 0\) is given by