Class CBSE Class 12 Mathematics Linear Programming Q #855
COMPETENCY BASED
APPLY
1 Marks 2023 MCQ SINGLE
The number of corner points of the feasible region determined by the constraints x-y\ge0, 2y\le x+2, x\ge0, y\ge0 is:
(A) 2
(B) 3
(C) 4
(D) 5
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Step-by-Step Solution

  1. Rewrite the inequalities:
    • x - y ≥ 0 => y ≤ x
    • 2y ≤ x + 2 => y ≤ (1/2)x + 1
    • x ≥ 0
    • y ≥ 0
  2. Graph the inequalities:
    • y ≤ x is the region below the line y = x.
    • y ≤ (1/2)x + 1 is the region below the line y = (1/2)x + 1.
    • x ≥ 0 is the region to the right of the y-axis.
    • y ≥ 0 is the region above the x-axis.
  3. Identify the feasible region: The feasible region is the intersection of all these regions.
  4. Find the corner points:
    • Intersection of y = x and x = 0: (0, 0)
    • Intersection of y = 0 and y = x: (0, 0)
    • Intersection of y = 0 and y = (1/2)x + 1: (0,0) is not on y = (1/2)x + 1. Solving y = 0 and y = (1/2)x + 1 gives 0 = (1/2)x + 1 => x = -2, which is not feasible since x >= 0.
    • Intersection of y = x and y = (1/2)x + 1: x = (1/2)x + 1 => (1/2)x = 1 => x = 2, so y = 2. The point is (2, 2).
    • Intersection of x = 0 and y = (1/2)x + 1: y = (1/2)(0) + 1 = 1. The point is (0, 1).
  5. The corner points of the feasible region are (0, 0), (2, 2), and (0, 1).
  6. Count the corner points: There are 3 corner points.

Correct Answer: 3

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AI Suggestion: Option B

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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 graphical methods to determine the feasible region and count its corner points.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of linear inequalities, feasible regions, and corner points in linear programming. It's not just about recalling facts but applying the concepts to solve the problem.
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 specific problem, rather than simply recalling definitions or theorems. It requires them to graph inequalities, identify the feasible region, and determine the corner points, which are all application-based skills.

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