Please show full work !!

70 35 9.17 (pape 383). Find the optimal shipment of cars that minimizes the total miles traveled. The following feasible plan is obtained by applying the Northwest Corner Rule To Coal Valley Coal Town CoalJunction Coals Burg FROM (1 7 (B) Supply Morgantown 3060 MO Youngstown 20 8 0 10 90 ( 40 20 60 Pittsburgh 100 40 30 Demand Total cost in miles) - 30450 mi.) + (30 m.) + 40480 mi.) 2010 m.) + 5(80 m.) + 2030 mi.) - 6,050 miles FROM Find the primal plan by using the Stepping Stone method To Coal Valley CoalTown Counction CoalsBurg 0 ( 0 0 (6) Morgantown 50 30 60 70 (M 5 1 00) 160) Youngstown 20 80 10 90 0 80) 1 20 130) Pittsburgh 100 00 0 30 0 -70 -110) 5 20 Demand I 30 45 25 20 The improvement indices are Wetermined as follows: Supply Krow Mfirst, then rows Yand P) M: 60-10-80-30-100 35 MB: 70-30+80-10+80-30 - 160 Y: 20-50-30-80 - 80 60 YR: 90-30+80-10-130 PV: 100-50+30 80+10-80 -70 25 PT: 40-80+10-80-110 120 the most negative index" We focus on cell PT (index=-110). Its closed path is: PT to PJ to YJ to YT, back to PT. To increase the quantity in PT, we need to adjust PJ down. YJ up, and YT down. Therefore, the next improved plan is (b) Determine the Indices: Supply Krow M first, then rows Y and P) 170 30 To FROM Morgantown (M Youngstown (9) Pittsburgh ( Demand Coal Valley CoalTown CoalJunction CoalsBurg (B) 50 30 60 5 20 80 10 9 0 25 100 40 80 20 45 25 20 35 60 30 120 (a) Find the new TC (in miles) - (show steps). (1) ke) Determine the Indices: Supply row Mfirst, then rows Y and P) 50 60 (c) Determine the next improved plan. To Coal Valley CoalTown CoalJunction CoalsBurg FROM Morgantown 30 (M) Youngstown 20 80 10 (2) Pittsburgh 100 40 (P Demand 45 25 20 (d) Find the new TC (in miles) - 120 (show steps). (This current solution is optimal as all improvement indices are (see p.352)