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Question
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. The Minimum value of F occurs at ______.
Options
(0, 2) only
(3, 0) only
The midpoint of the line segment joining the points (0, 2) and (3, 0) only
Any point on the line segment joining the points (0, 2) and (3, 0).
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Solution
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. The Minimum value of F occurs at any point on the line segment joining the points (0, 2) and (3, 0).
Explanation:
| Corner points | Value of F = 4x + 6y | |
| (0, 2) | Z = 4(0) + 6(2) = 12 | ← Minimum |
| (3, 0) | Z = 4(3) + 6(0) = 12 | ← Minimum |
| (6, 0) | Z = 4(6) + 6(0) = 24 | |
| (6, 8) | Z = 4(6) + 6(8) = 72 | ← Maximum |
| (0, 5) | Z = 4(0) + 6(5) = 30 |
The minimum value of F occurs at any point on the line segment joining the points (0, 2) and (3, 0).
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