State which of the following statements are true and which are false.

Question

State which of the following statements are true and which are false. Give reasons for your answer with a short proof or a counter example.

a) The intersection of finite number of convex sets is not convex.

b) If value of the 2× 2 matrix game $\begin{bmatrix}1&2\\p&4\end{bmatrix}$ is 4, then p ≥ 4 .

c) If 10 is added to each of the entries of the cost matrix of a 3× 3 assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.

d) For maximization LP model, the simplex method is terminated when all values c_j − z_j ≥ .0

e) The dummy source or destination in a transportation problem is added to prevent solution from becoming degenerate.

20 Feb 2025

Answer :

Word Count : 201

a) False. The intersection of a finite number of convex sets is always convex. If two points belong to the intersection of convex sets, then the line segment joining them remains within each convex set, thus remaining in the intersection.

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	A	B	C	D
I	14	18	11	26
III	17	23	20	27
III	28	31	26	30
IV	23	3	25	28

90	90	100	110	200
50	70	130	85	50
75	100	100	30