Question:
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 :
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 :
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Always double-check your arithmetic for each vertex. In LPP, the optimal solution is guaranteed to be at a corner point, so you don't need to check any interior points.
Updated On: Sep 10, 2026
- \( 200 \)
- \( 300 \)
- \( 240 \)
- \( 120 \)
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The Correct Option is B
Solution and Explanation
Concept:
• Corner Point Theorem: The maximum or minimum value of an objective function in a Linear Programming Problem occurs at one of the corner points (vertices) of the feasible region.
Step 1: Evaluate the objective function at each corner point
Objective Function: \( Z = 4x + 3y \).
Calculate \( Z \) for each given point:
1. For \( (0, 0) \): \( Z = 4(0) + 3(0) = 0 \)
2. For \( (0, 40) \): \( Z = 4(0) + 3(40) = 120 \)
3. For \( (20, 40) \): \( Z = 4(20) + 3(40) = 80 + 120 = 200 \)
4. For \( (60, 20) \): \( Z = 4(60) + 3(20) = 240 + 60 = 300 \)
5. For \( (60, 0) \): \( Z = 4(60) + 3(0) = 240 \)
Step 2: Identify the maximum value from the results
Compare all calculated values of \( Z \):
\[ \{0, 120, 200, 300, 240\} \]
The largest value among these is 300, which occurs at the point \( (60, 20) \).
• Corner Point Theorem: The maximum or minimum value of an objective function in a Linear Programming Problem occurs at one of the corner points (vertices) of the feasible region.
Step 1: Evaluate the objective function at each corner point
Objective Function: \( Z = 4x + 3y \).
Calculate \( Z \) for each given point:
1. For \( (0, 0) \): \( Z = 4(0) + 3(0) = 0 \)
2. For \( (0, 40) \): \( Z = 4(0) + 3(40) = 120 \)
3. For \( (20, 40) \): \( Z = 4(20) + 3(40) = 80 + 120 = 200 \)
4. For \( (60, 20) \): \( Z = 4(60) + 3(20) = 240 + 60 = 300 \)
5. For \( (60, 0) \): \( Z = 4(60) + 3(0) = 240 \)
Step 2: Identify the maximum value from the results
Compare all calculated values of \( Z \):
\[ \{0, 120, 200, 300, 240\} \]
The largest value among these is 300, which occurs at the point \( (60, 20) \).
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