2. (18) The data for a transportation problem is summarized below. Given are the matrix of costs [cij], si the available supply for each supply node i, and d; the demand for each demand node j. 1 2 3 | d; 1 6 4 3 10 2 2 2 1 10 3 -1 2 2 20 4 | si 0 5 3 25 1 25 15 (a) Find an initial basic feasible solution using Vogel's method. (b) Specify the dual problem. This problem is continued on the next page. 2.(continued) (c) Consider the solution X = [Xij] 7 1 2 3 4 si 16 2 -1 0 5 2 4 2 2 3 25 3 3 1 2 1 25 di 10 10 20 15 | T0 0 X = [Xijl= | 0 10 | 10 0 5 15 0 0 0 15 Is this solution a basic feasible solution? If so, specify the basic variables. If not, find one. (d) Is this solution optimal? Justify your answer and show your work