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Question #41280

Difficulty: 8/10 | 🟢 Free

The Question

Consider the linear programming problem: Maximize $Z = \begin{pmatrix} 4 & -3 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$ subject to the constraints: $\begin{pmatrix} 2 & 1 \\ 4 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} \le \begin{pmatrix} 5 \\ 13 \end{pmatrix}$ $x \ge 0, y \ge 0$ The maximum value of $Z$ is:

Options

A.
15
B.
10
C.
13
D.
0

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

Cramer's Rule Constraints|Objective Function Gradient|Non-Negativity Restriction

Why This Question Is Tricky

Common Mistakes

This question tests the student's vigilance regarding non-negativity constraints in Linear Programming Problems (LPP).

A common trap is to blindly solve the system of boundary equations (often using Cramer's rule or matrix inversion) to find the intersection point, assuming it to be the optimal vertex.

Here, the intersection point $(3, -1)$ yields a tempting maximum value of 15, which is provided as a distractor.

However, this point violates the $y \ge 0$ condition.

Students must graph or algebraically verify the feasible region to realize that one constraint is redundant in the first quadrant, and the true maximum lies on the x-axis.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Determinants - Class 12
Concept	Cramer's Rule Constraints
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free