21. (50 pts) Given the network representation below, you are trying to find the shortest distance between your home (node h) to destination (node d). The minimum spanning tree for the network is given as arcs (1,1), (1,3), (2,5), (3,5), (5,4), (4,d), (6,d) and only created by basic variables. There are not any NBV at Upper Bound in the MST. Distances for the arcs are given in the table. Hint: All variables (x_ij's) E (0,1) where i E {h,1,2,3,4,5,6), j E {1,2,3,4,5,6,d) a) Draw the minimum spanning tree (MST). b) Use network simplex algorithm to determine whether the solution that you obtained in MST is optimal? If not, what are the entering and leaving variables and the value of 0(theta)? - Don't solve for optimal! (h.1) (h.2) (h.3) (1,4 (1,5) (2,4 2,5 (3,5) (3,6) (4.d) (5,4) (5,6) (5,d) (6,d) Distance 1252 1470 1132 1126 429 770 553 1296 1089 533 1402 874 959 1514