MHT CET · Maths · Straight Lines

The vertices of the feasible region for the constraints \(x+y \leq 4, x \leq 2, y \leq 1, x+y \geq 1, x\), \(y \geq 0\) are

A (1,0),(2,0),(2,1),(0,4)
B (0,1),(4,0),(0,4),(1,0)
C (1,0),(2,0),(2,1),(0,1)
D (1,0),(4,0),(2,1),(0,4)

Verified Solution

Answer & Solution

Correct Answer

(C) (1,0),(2,0),(2,1),(0,1)

Step-by-step Solution

Detailed explanation

Feasible region lies on origin side of \(x+y=4\), \(x=2, y=1\) and non-origin side of \(x+y=1\) and in first quadrant.
\(\therefore\) Vertices of feasible region are \(\mathrm{A}(1,0), \mathrm{B}(2,0), \mathrm{C}(2,1), \mathrm{D}(0,1)\)

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.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app