Before You Begin

Question #41772

Difficulty: 8/10 | 🟢 Free

The Question

Consider the feasible region $S = \{ (x, y) \in \mathbb{R}^2 : x \ge 3, \ xy - x^2 - 2y + 3 \ge 0 \}$ . If $m$ is the infimum of the objective function $Z = 2y - 2x + 5$ on the region $S$ , then the value of $m$ is:

Options

A.
9
B.
11
C.
10
D.
8

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|Unbounded Region Trap|Rational Function Asymptotes

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle optimization over unbounded feasible regions with non-linear (rational) boundaries.

The primary trap is the assumption that the optimal value (infimum) must occur at a vertex of the feasible region, a habit formed from standard Linear Programming.

By introducing a hyperbola with a slant asymptote, the objective function's gradient aligns such that it strictly decreases along the unbounded direction.

Students who merely check the vertex $(3,6)$ will incorrectly conclude the minimum is 11, missing the asymptotic infimum of 9.

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