COMEDK · Maths · 35. Linear Programming

For a given Linear Programming problem, the objective function is
\(Z=3 x+2 y\)
Subject to constraints are
\(\begin{aligned}
& 4 x+3 y \leq 60 \\
& x \geq 3 \\
& y \leq 2 x \\
& y \geq 0
\end{aligned}\)
P is one of the corner points of the feasible region for the given Linear Programming problem. Then the coordinate of P is

A \((0,0)\)
B \((12,6)\)
C \((0,20)\)
D \((3,6)\)

Verified Solution

Answer & Solution

Correct Answer

(D) \((3,6)\)

Step-by-step Solution

Detailed explanation

The feasible region is defined by the constraints \(4x + 3y \leq 60\), \(x \geq 3\), \(y \leq 2x\), and \(y \geq 0\). First, identify the intersection points of the boundary lines: 1. The line \(x = 3\) intersects \(y = 0\) at \((3, 0)\). 2. The line \(x = 3\) intersects…

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 COMEDK

Explore more questions on app