Class CBSE Class 12 Mathematics Linear Programming Q #679
COMPETENCY BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
In a Linear Programming Problem (LPP), the objective function \(Z=2x+5y\) is to be maximised under the following constraints: \(x+y\le4\), \(3x+3y\ge18\), \(x, y\ge0\). Study the graph and select the correct option. The solution of the given LPP:

[Image Missing]
(A) lies in the shaded unbounded region.
(B) lies in \(\Delta AOB\).
(C) does not exist.
(D) lies in the combined region of \(\Delta AOB\) and unbounded shaded region.
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Correct Answer: C

AI Tutor Explanation

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Step-by-Step Solution

Let's analyze the constraints:

  1. \(x + y \le 4\)
  2. \(3x + 3y \ge 18\), which simplifies to \(x + y \ge 6\)
  3. \(x, y \ge 0\)

Notice that the constraints \(x + y \le 4\) and \(x + y \ge 6\) are contradictory. There are no values of \(x\) and \(y\) that can simultaneously satisfy both inequalities.

Therefore, there is no feasible region, and the solution to the LPP does not exist.

Correct Answer: does not exist.<\/strong>

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply their understanding of linear programming constraints and feasible regions to determine the solution's existence based on a graph (which is missing, but the question implies its existence).
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of concepts related to linear programming, such as constraints, feasible regions, and the existence of solutions. It requires the student to interpret the graphical representation of these concepts.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question requires the student to apply the concepts of LPP to analyze a given scenario and choose the correct option, rather than simply recalling a definition or formula.

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