State whether the following statements are True or False and also give the reason in support of your answer.
a) The Set $ ={(x, y) : 0 ≤ y ≤ 5 when 0 ≤ x≤ 2 and 3≤ y≤ 5 when 2≤ x ≤ 7 } is not a convex set.
b) If 10 is added to each of the entries of the cost matrix of a 3 x 3 assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.
c) The solution to a transportation problem with m-rows (supplies) and n-columns (destinations) is feasible if number of positive allocations is m + n.
d) The Value di ≥ 3 indicates an outlying observation in regression analysis.
e) Variations which occur due to natural forces and operate in a regular and periodic manner over a span of less than or equal to one year are termed as cyclic variations

a) True. The given set is not a convex set because it is not closed under line segments. For example, the line segment joining points $(0,0)$ and $(2,3)$ lies entirely within the set, but the midpoint of the line segment $((0+2)/2, (0+3)/2) = _______ ____ ___ __________ ___ ____ ______ _________.
__________ ______ _____ ___ ____ ___ _____ ___ ______ _________ ___.
_____ _______ ________ _____ ____ ________ __________ ___ __________ ____ ____ __________.
_________ ______ _______ _______ _________ ________ _________.
_____ ____ ____ ______ ___ ____.
____ __________ ________ _______ __________ _______ ____ __________ ______ ______ _______ __________.
________ _______ ________ __________ __________ ____ __________ _________ _______ ________.
_________ _______ _____ ___ _________ ___ ____ _______.
___ __________ ________ _____ ____.
_____ __________ _________ ______ ________ ______ ____ __________ __________ ________ ________.
_________ __________ _____ _______ ________ ____ ______ _______ ________.
______ _____ ________ _________ ______ ______ ____.
________ ___ __________ _____ ___ ___ _________ __________ ____.
_____ ____ ____ _____ ___ _________ ________ ________ __________ ___ ____.
_____ __________ ______ ___ ____.
___ ________ _____ ___ ____ ____ ____ _________ _____ ________ ____.
_________ ________ _____ ___ _________ ___ __________.
____ ____ _________ ___ _________.
___ ___ ____ ___ _________ _______ __________.
_________ ___ ____ ________ _________ __________ _________ ____.
______ __________ ___ ____ ___ _______ _______ ___ ______ _________ ______.
____ ______ ______ _________ __________ ________ ________.
___ __________ __________ _________ ____.
______ __________ ________ _______ ______.
_____ _______ __________ _________ ________ ___ ________ ______ _________ ________ _____ _________.
__________ __________ ___ __________ ________ _____ _______.
Get Full Answer on WhatsApp