(2) Find an optimal solution for the following transportation problem. Valley Town Junction FROM Supply Madison (M Yonkers S Ss 300 52 ( Pittsburgh 50 53 50 38 400 59 SIL 200 sto 600 Demand 33 300 450 200 250 250 The above feasible plan (ie, 300 from M to V, etc.) is obtained by applying the Northwest Corner Rale, und 200 1.200 its total cost - 300455) + 50(53) + 400458) +20051) 504580) 200x530) - 56.050 Using the Stepping-Stone method to find an optimal plan To Valley Town The improvement indices) FROM Junction Burg bare determined as follows (D (B) Madison SS $3 Supply Crow Mflest, the ows You 56 (M) MU: 6-148-3-19 300 50 350 MB: 7-3-8-18-3-16 Yonkers $2 S8 SI 59 YV: 2-5-3-8- 0 400 200 600YB: 9-3 +8-1-13 $11 $8 $3 Pittsburgh P: 11-5-3-8+1-8- (P) 50 200 250 PT: 10-8-1- Demand 300 450 250 200 1.200 the most negative index" $10 We focus on cell YV (index --8). Its closed path is: YV to MV to MT to YT, back to YV. To increase the quantity in YV, we need to adjust MV down, MT up, and YT down. Therefore, the next improved plan is: Valley Town Junction Burg FROM Part b) Determine the Indices U Supply_row first, then rows Yand Madison 35 $3 $6 $7 (M) 350 350 Yonkers 32 S8 SI $9 300 100 200 600 $11 $10 S8 53 Pittsburgh 50 200 250 (P 200 450 250 1.200 Asterisk the most negative index 300 Demand (show steps) Part a) Find the new TC= Burg (8) Parte) Determine the Indices: Supply row first, then rows Tand) $7 350 53 ss Part c) Determine the next improved plan. Valley Town Junction FROM ( 0 Madison $6 M S8 S2 $1 Yonkers $9 600 $3 S8 250 1,200 scrisk the most negative index (show steps) 200 250 (hint: see p.352) Pittsburgh SIT S10 (P2 Demand 300 450 Part d) Find the new TC - Part Is the current solution optimal