(2) Find an optimal solution for the following transportation problem. To Valley Town (5 (7) FROM Madison (35) Yonkers (3 Pittsburgh 10 Demand 350 FROM To Valley (155) 350 Madison (M) Yonkers Madison (M) Yonkers (35 Pittsburgh FROM Using the Stepping Stone method to find an optimal plan, Town Junction Madison The above feasible plan is obtained by applying the Northwest Corner Rule (eg, 300 from M to V, etc.), and its total cost 350(58) +50(510)+150(512)+250(54)+200($11)+250(514)-SIL800 Yonkers SK Pittsburgh 10 Demand SIS 350 Valley (5) 50 150 SK 58 50 150 $10 150 56 Town (7) $10 Demand Part(a) Find the new TC Part(e) Determine the next improved plan, To Valley (52) 200 $6 Town (7) $10 Pittsburgh Demand 200 250 We focus on cell PT (index=9). Its closed path is: PT to PB to Y to YT, and back to PT. To increase the quantity in PT, we need to adjust PB down, Yup, and YT down. Therefore, the next improved plan is To $6 Junction Burg (8) $10 Part (d) Find the new TC = Part() is the current solution optimal? 250 $11 Junction (5) 250 200 250 450 Junction Explain 314 Burg (8) 200 250 450 100 56 $14 Burg (85 Burg (8) Supply 400 250 1,250 56 Supply 400 600 250 1.250 The improvement indices below are determined as follows: row M first, then sows and P) MA: 9-4+12-10-2 MB: 6-11-12-10 5-12+10-8-8- 400 PP: 15-14-11-12-10-8 PT: 6-14+11-12-2 PA 11-14+11-4-4 Part (b) Find the indices (show steps) Supply Row Mf first, then sows and P the "most negative index" 600 600 250 1.250 Asterisk the "most negative index" (show steps) Part (e) Find the indices (show steps) Supply Row Mf first, then rows and P 400 250 1.250 Asterisk the "most negative index" (show steps).