Consider minimize z=c_Tx
subject to Ax=b
And if x* is the optimal soltuion for the primal and y*is the optimal solution for the dual, describe what effect on they have on x*and y*
these changes should be considered indivually.

1.the vector c is multiplied by t, where t >0
2.the k-th equality constraint is multiplied by t
3.the i-th equality constraint is modified by adding to it t times the k-th equality constraint
4. the right had side b is multiplied by t