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  • 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 A. (0, 2) only B. (3, 0) only C. the midpoint of the line segment joining the points

Q: 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
A. (0, 2) only
B. (3, 0) only
C. the midpoint of the line segment joining the points (0, 2) and (3, 0) only
D. any point on the line segment joining the points (0, 2) and (3, 0).

Answers (1)

Correct Answer D)
Answer:
F = 4x + 6y
Corner points - (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).
Value of F at corner points –
At (0, 2), F = 12
At (3, 0), F = 12
At (6, 0), F = 24
At (6, 8), F = 72
At (0, 5), F = 30
Feasible region –
As, feasible region to be bounded so it is a closed polygon.
So, minimum values of F = 12 are at (3, 0) and (0, 2).
Therefore, 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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