GATE ME 2018 Set 1 — Question 61
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Industrial Engineering → Operations Research → LP (Graphical & Simplex)
Last updated
Question
The minimum value of
such that:
is _______.
such that:
is _______.
Correct answer
0 to 0
Solution
We are asked to minimize the objective function subject to the given constraints.Constraints:
1)
2)
3)
4) The feasible region is a convex polygon in the first quadrant. We check if the origin is in the feasible region:
1) (True)
2) (True)
3) (True)
Since satisfies all constraints, it is a feasible point.For an objective function where , the minimum value in a feasible region that includes the origin and is restricted to the first quadrant will occur at the origin .At :
Since and , can never be less than . Thus, the minimum value is .
1)
2)
3)
4) The feasible region is a convex polygon in the first quadrant. We check if the origin is in the feasible region:
1) (True)
2) (True)
3) (True)
Since satisfies all constraints, it is a feasible point.For an objective function where , the minimum value in a feasible region that includes the origin and is restricted to the first quadrant will occur at the origin .At :
Since and , can never be less than . Thus, the minimum value is .
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