Answer to Question #106118 in Operations Research for Anu

Question

State which of the following statements are true and which are false. Give reasons for
your answers with a short proof or a counter-example. (10)
i) The set of all convex combinations of a finite number of points 1 2 Xn X is not ,X ,...,
a convex set.
ii) If the pay-off matrix of a game is transformed, saddle point of the game if it exists,
changes.
iii) If a negative value appears in the solution values ) (XB
column of the simplex
method, then the basic solution is optimum.
iv) In an assignment problem, if a constant is added to each element of the matrix, the
optimal assignment does not change.
v) In an LPP, every feasible solution is optimal.

Answer 1

(i)True,because a set is said to be convex set if and only if it contains all the convex combination of all its elements.

(ii)False,If the pay-off matrix of a game is transformed, saddle point of the game if it exists,does not change because all the elements of the pay off matrix change by equal amount.So,element which was smaller still remains smaller and element which was larger still remains larger.

(iii)True, If a negative value appears in the solution column of the simplex method, then the basic solution is optimum.

(iv)True,In an assignment problem, if a constant is added to each element of the matrix, the optimal assignment does not change, because all the elements of the matrix change by equal amount.So,element which was smaller still remains smaller and element which was larger still remains larger.

(v)False, because in an LPP some of the feasible solution is an optimal solution.