Class CBSE Class 12 Mathematics Linear Programming Q #1733
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
The corner points of the feasible region determined by the system of linear constraints are (0,0), (0, 40), (20, 40), (60, 20) and (60, 0). If the objective function of an LPP is $Z=4x+3y$, then the maximum value is :
(A) 200
(B) 300
(C) 240
(D) 120
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Correct Answer: B

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Detailed Solution

Step 1: Identify the Objective Function

The objective function is given by Z = 4x + 3y. We need to evaluate this function at each of the provided corner points of the feasible region.

Step 2: Evaluate Z at each corner point

We substitute the coordinates (x, y) into the objective function:

  • At (0, 0): Z = 4(0) + 3(0) = 0
  • At (0, 40): Z = 4(0) + 3(40) = 120
  • At (20, 40): Z = 4(20) + 3(40) = 80 + 120 = 200
  • At (60, 20): Z = 4(60) + 3(20) = 240 + 60 = 300
  • At (60, 0): Z = 4(60) + 3(0) = 240

Step 3: Determine the Maximum Value

Comparing the calculated values {0, 120, 200, 300, 240}, the maximum value is 300, which occurs at the point (60, 20).

Final Answer: 300

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must utilize the Corner Point Method to solve a Linear Programming Problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the execution of a specific algorithmic process (evaluating an objective function at vertices) to reach the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This question tests the student's ability to apply optimization techniques in LPP, which is a core competency in the Linear Programming chapter.
||KEY:B

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