Before You Begin
Question #41780
The Question
Let be the feasible region in the -plane defined by the inequalities , , and . Consider the objective function What is the absolute minimum value of on the region ?
Options
- A.
4
- B.
6
- C.
5
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Bridge
Practice problems that bridge the gap between foundational theory and advanced practical application.
Concepts Behind This Question
Non-Negativity Restriction|Non-Differentiable Extrema|Modulus Function Breakdown
Why This Question Is Tricky
Common Mistakes
This question exploits a deeply ingrained bias from standard Linear Programming: the assumption that the extrema of an objective function always occur at the vertices of the feasible region.
By introducing a modulus term, the objective function becomes piecewise linear and non-differentiable along a cusp line.
The 'Lethal Collision' occurs because the true minimum lies on a boundary segment exactly where this cusp line intersects it, rather than at a primary vertex.
Students who blindly apply the vertex evaluation method will incorrectly conclude the minimum is 6, falling directly into the trap.
Quick Facts About This Question
Question Information
| Subject | Mathematics |
| Chapter | Linear Programming - Class 12 |
| Concept | Non-Negativity Restriction |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |