Class CBSE Class 12 Mathematics Linear Programming Q #854
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
The corner points of the feasible region in the graphical representation of a linear programming problem are (2, 72), (15, 20) and (40, 15). If z=18x+9y be the objective function, then :
(A) z is maximum at (2, 72), minimum at (15, 20)
(B) z is maximum at (15, 20), minimum at (40, 15)
(C) z is maximum at (40, 15), minimum at (15, 20)
(D) z is maximum at (40, 15), minimum at (2, 72)
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Step-by-Step Solution

  1. Evaluate the objective function z = 18x + 9y at each corner point:

  2. At (2, 72): z = 18(2) + 9(72) = 36 + 648 = 684

  3. At (15, 20): z = 18(15) + 9(20) = 270 + 180 = 450

  4. At (40, 15): z = 18(40) + 9(15) = 720 + 135 = 855

  5. Compare the values of z at each point:

    • Maximum value of z is 855 at (40, 15)
    • Minimum value of z is 450 at (15, 20)

Correct Answer: z is maximum at (40, 15), minimum at (15, 20)

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of evaluating the objective function at corner points to find the maximum and minimum values.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (evaluating the objective function at each corner point) to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of the linear programming concepts taught in the textbook.

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