Before You Begin

Question #41676

Difficulty: 8/10 | 🟢 Free

The Question

Let $S$ be the feasible region in the $xy$ -plane defined by the inequalities: $y - |2x - 4| \ge 0$ $2x - y + 2 \ge 0$ Find the maximum value of the objective function $Z = 5x - 2y$ on the region $S$ .

Options

A.
10
B.
12
C.
$-\frac{7}{2}$
D.
Does not exist

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Unbounded Region Trap|Corner Point Method Precision|Right-Hand vs Left-Hand Derivatives

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of Linear Programming principles, specifically targeting the blind use of the Corner Point Method.

Students frequently identify the vertices of a feasible region, evaluate the objective function, and declare the highest value as the maximum.

Here, the region is a semi-infinite strip.

The lower boundary has a non-differentiable cusp at $(2,0)$ where the Left-Hand Derivative is -2 and the Right-Hand Derivative is 2.

Because the slope of the objective function ( $Z = 5x - 2y \implies m = 2.5$ ) exceeds the RHD of the boundary, the level curves of $Z$ intersect the unbounded ray $y = 2x - 4$ at increasingly larger values.

The student is trapped into choosing $Z=10$ at the cusp, failing to realize the region is unbounded in a direction that allows $Z \to \infty$ .

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Programming - Class 12
Concept	Unbounded Region Trap
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free