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Question #41775

Difficulty: 8/10 | 🟢 Free

The Question

Consider the linear programming problem: Maximize $Z = 2x + 5y$ Subject to the constraints: $|x - 2| + |y - 3| \le 4$ $4x + y \le 10$ $x \ge 0, y \ge 0$

The maximum value of $Z$ is:

Options

A.
32
B.
44
C.
45
D.
50

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

Objective Function Gradient|Redundant Constraints|Modulus Sign Dependency

Why This Question Is Tricky

Common Mistakes

This question deploys the 'Modulus Sign Dependency' trap.

Students frequently drop the absolute value bars, incorrectly simplifying the first constraint to $x + y \le 9$ .

This expands the feasible region to include phantom vertices such as $(0,9)$ and $(1/3, 26/3)$ .

The objective function $Z = 2x + 5y$ has a gradient that heavily favors the y-axis, deliberately pointing towards these phantom vertices to yield trap answers like 45 or 44.

Alternatively, ignoring the diamond entirely yields the y-intercept of the second constraint $(0,10)$ , giving 50.

To solve this, candidates must rigorously evaluate the piecewise linear boundaries of the modulus function and find the true intersection at $(1,6)$ .

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Programming - Class 12
Concept	Objective Function Gradient
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free