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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In LPP problems, usually, points with a mix of high values for both variables (like \( 60, 20 \)) are likely candidates for the maximum if coefficients are positive.
Always organize your evaluations in a table to avoid simple calculation errors.
Always organize your evaluations in a table to avoid simple calculation errors.
Updated On: Sep 10, 2026
- \( 200 \)
- \( 300 \)
- \( 240 \)
- \( 120 \)
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The Correct Option is B
Solution and Explanation
Concept:
• Corner Point Method: For a bounded feasible region, the optimal (maximum or minimum) value of the objective function occurs at one of the corner points.
• Evaluate \( Z \) at every given corner point and choose the largest value.
Step 1: Calculate \( Z \) at each corner point
Objective function: \( Z = 4x + 3y \).
• 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 2: Compare the values and identify the maximum
The values calculated are \( \{0, 120, 200, 300, 240\} \). The highest value among these is \( 300 \).
Step 3: Conclusion
The maximum value of \( Z \) is \( 300 \), which occurs at the point \( (60, 20) \). This matches option (B).
• Corner Point Method: For a bounded feasible region, the optimal (maximum or minimum) value of the objective function occurs at one of the corner points.
• Evaluate \( Z \) at every given corner point and choose the largest value.
Step 1: Calculate \( Z \) at each corner point
Objective function: \( Z = 4x + 3y \).
• 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 2: Compare the values and identify the maximum
The values calculated are \( \{0, 120, 200, 300, 240\} \). The highest value among these is \( 300 \).
Step 3: Conclusion
The maximum value of \( Z \) is \( 300 \), which occurs at the point \( (60, 20) \). This matches option (B).
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