Class CBSE Class 12 Mathematics Linear Programming Q #835
COMPETENCY BASED
APPLY
1 Marks 2023 MCQ SINGLE
The feasible region of a linear programming problem is shown in the figure below: ... Which of the following are the possible constraints?
(A) $x+2y\ge4, x+y\le3, x\ge0, y\ge0$
(B) $x+2y\le4, x+y\le3, x\ge0, y\ge0$
(C) $x+2y\ge4, x+y\ge3, x\ge0, y\ge0$
(D) $x+2y\ge4, x+y\ge3, x\le0, y\le0$
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Step-by-Step Solution

  1. Analyze the graph:<\/strong> The feasible region is bounded by lines. We need to determine the inequalities that define this region.
  2. Consider the line x + 2y = 4:<\/strong> The line passes through (4,0) and (0,2). The feasible region lies above this line. Therefore, the inequality is x + 2y ≥ 4.
  3. Consider the line x + y = 3:<\/strong> The line passes through (3,0) and (0,3). The feasible region lies below this line. Therefore, the inequality is x + y ≤ 3.
  4. Consider the non-negativity constraints:<\/strong> Since the feasible region is in the first quadrant, x ≥ 0 and y ≥ 0.
  5. Combine the inequalities:<\/strong> The constraints are x + 2y ≥ 4, x + y ≤ 3, x ≥ 0, and y ≥ 0.
  6. Match with the options:<\/strong> Option (A) matches the derived constraints: x + 2y ≥ 4, x + y ≤ 3, x ≥ 0, y ≥ 0.

Correct Answer: x+2y\ge4, x+y\le3, x\ge0, y\ge0

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their understanding of linear inequalities and feasible regions to determine the correct constraints based on a given graph.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to apply a procedure to identify the correct constraints from a given feasible region. This involves testing points and understanding the graphical representation of inequalities.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question assesses the student's ability to apply the concepts of linear programming to a visual representation and select the correct constraints, rather than simply recalling definitions or theorems.

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