Linear Programming Question 115
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:
A) $ (0,2) $ Only
B) $ (3,0) $ Only
C) The mind-point of the line segment joining the points $ (0,2) $ and $ (3,2) $ only
D) Any point on the line segment joining the points $ (0,2) $ and $ (3,0) $
Show Answer
Answer:
Correct Answer: D
Solution:
Construct the following table of objective function
| Corner point | Value of $ F=4x+6y $ | |||
| (0, 2) | $ 4\times 0+6\times 2=12 $ | |||
| (3, 0) | $ 4\times 3+6\times 0=12 $ | |||
| (6, 0) | $ 4\times 6+6\times 0=24 $ | |||
| (6, 8) | $ 4\times 6+6\times 8=72 $ | |||
| (0, 5) | $ 4\times 0+6\times 5=30 $ |
}←minimum }←maximum
Since the minimum value (F) =12 occurs at two distinct corner points, it occurs at every points of the segment joining these two points.
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