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Question #40552

Difficulty: 8/10 | 🟢 Free

The Question

Consider the feasible region $R$ in the $xy$ -plane determined by the following system of inequalities: $|x - 2y| \le 4$ $x + y \le 6$ $x \ge 0, y \ge 0$ Find the maximum value of the objective function $Z = 4x + 7y$ over the region $R$ .

Options

A.
34
B.
42
C.
26
D.
24

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

Graphical Feasible Region|Corner Point Method Precision|Non-Negativity Restriction|The Modulus Trap

Why This Question Is Tricky

Common Mistakes

This question tests the precision of the Corner Point Method when dealing with modulus-based linear inequalities.

The 'Modulus Trap' requires students to bifurcate $|x - 2y| \le 4$ into two distinct boundary lines and perform a strict Boolean 'AND' operation with the non-negativity constraints.

A common lethal mistake is blindly evaluating the objective function at all pairwise intersections of the boundary lines (such as the y-intercept of $x+y=6$ , which is $(0,6)$ ) without verifying if those points lie within the true feasible region.

Doing so yields a phantom maximum of $Z=42$ , effectively punishing students who bypass the graphical verification of the polygon's vertices.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Inequalities - Class 11
Concept	Graphical Feasible Region
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free