Class CBSE Class 12 Mathematics Linear Programming Q #684
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
If the feasible region of a linear programming problem with objective function \(Z = ax + by\), is bounded, then which of the following is correct?
(A) It will only have a maximum value.
(B) It will only have a minimum value.
(C) It will have both maximum and minimum values.
(D) It will have neither maximum nor minimum value.
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Correct Answer: C

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Step-by-Step Solution

If the feasible region is bounded, it means the region is enclosed and finite. In linear programming, the maximum and minimum values of the objective function occur at the corner points of the feasible region.

For a bounded feasible region, we evaluate the objective function at each corner point. The largest value is the maximum, and the smallest value is the minimum.

Therefore, if the feasible region is bounded, the objective function will have both a maximum and a minimum value.

Correct Answer: It will have both maximum and minimum values.

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to comprehend the properties of a feasible region in linear programming and its implications for the objective function's maximum and minimum values.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of bounded feasible regions and their relationship to the existence of maximum and minimum values of the objective function.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of the theoretical concepts related to linear programming as covered in the textbook.

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