MHT CET · Maths · Linear Programming

For the following shaded region the linear constraints are

A \(5 x+9 y \leq 90, x+y \geq 4, \quad y \geq 8, \quad x, y \geq 0\)
B \(5 x+9 y \geq 90, x+y \leq 4, \quad y \leq 8, \quad x, y \geq 0\)
C \(5 x+9 y \geq 90, x+y \geq 4, \quad y \geq 8, \quad x, y \geq 0\)
D \(5 x+9 y \leq 90, x+y \geq 4, \quad y \leq 8, \quad x, y \geq 0\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(5 x+9 y \leq 90, x+y \geq 4, \quad y \leq 8, \quad x, y \geq 0\)

Step-by-step Solution

Detailed explanation

Solution of \(5 x+9 y \leq 90\) is origin side, solution of \(x+y \geq 4\) is non-origin side and solution of \(y \leq 8\) is origin side

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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