Before You Begin

Question #41689

Difficulty: 8/10 | 🟢 Free

The Question

Let $R$ be the feasible region in the $xy$ -plane defined by the system of inequalities: $x + y \le 10, \quad x \le 7, \quad y \le 8, \quad 2x + 3y \le 30, \quad x \ge 0, \quad y \ge 0$ Consider the objective function $Z = 20 - |x - 2y + 5| - |2x + y - 10|$ . If $M$ is the global maximum value of $Z$ over the region $R$ , and it is attained at the point $(x_0, y_0)$ , then the value of $M + x_0 + y_0$ is

Options

A.
27
B.
19
C.
24
D.
16

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Monster

Ultra-high difficulty questions designed to test your limit, stamina, and deep conceptual understanding.

Concepts Behind This Question

Redundant Constraints|Geometry Constraint Modeling|Non-Differentiable Extrema|Global Extrema on Intervals

Why This Question Is Tricky

Common Mistakes

This question tests the 'Lethal Collision' between Linear Programming (LPP) feasible regions and non-differentiable concave topological analysis.

Students are heavily conditioned to evaluate objective functions exclusively at the vertices of the feasible region (standard Simplex/Vertex method logic).

The trap is set by providing a standard LPP constraint list (including a redundant constraint to distract and consume time) while the objective function is concave.

The global maximum actually occurs at an interior non-differentiable cusp.

Students who blindly test the vertices will find a false maximum of 9 at the vertex (2,8) and incorrectly choose 19, completely missing the interior critical point.

Quick Facts About This Question

Question Information

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