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Question #41767

Difficulty: 8/10 | 🟢 Free

The Question

Let $R$ be the feasible region in the $xy$ -plane defined by the inequalities $x \ge 0$ , $y \ge 0$ , and $x + y \le 25$ . Find the maximum value of the objective function $Z(x,y) = 2x + y - 3|x-4|^{2/3}$ over the region $R$ .

Options

A.
25
B.
27
C.
29
D.
31

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

Feasible Region Constancy|Increasing/Decreasing Strictness|Second Derivative Test Limitations

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to optimize a non-linear function over a constant feasible region while avoiding the trap of relying solely on the first derivative test ( $f'(x) = 0$ ).

Students commonly differentiate the objective function and find the smooth critical point at $x=12$ , yielding a sub-optimal value of 25.

By embedding an absolute value fractional power, the true global maximum is placed at a non-differentiable cusp ( $x=4$ ).

This penalizes algorithmic calculus application and rewards rigorous checking of all critical points, including boundaries and points of non-differentiability.

Quick Facts About This Question

Question Information

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