(2) Find an optimal solution for the following transportation problem. Tol Valley Town Junction Burg FROM ( (T) (J) (B) Supply Macon $6 $8 $7 $4 (M) 300 50 350 York $3 $10 $2 $9 ( 150 250 200 600 Perry $14 $4 $9 $12 (P) 250 250 Demand 300 200 250 450 1,200 The above feasible plan is obtained by applying the Northwest Corner Rule (e.g., 300 from M to V, etc.), and its total cost = 300($6) + 50($8) + 150($10) + 250($2) + 200($9) + 250($12) = $9,000. Using the Stepping-Stone method to find an optimal plan. The improvement indices below Tol Valley Town Junction Burg Jare determined as follows: FROM ( (T) (J (B) Supply(row M first, then rows Y and P) Macon $6 $8 $7 $4 MJ: 7-2+10-8 = 7 (M 300 50 350 MB: 4-9+10-8 = -3 York $3 $10 $2 $9 YV: 3-10+86=-5 (Y) 150 250 200 600 PV: 14-12-9-10+86 = 3 Perry $14 $4 $9 $12 PT: 4-12-9-10 = -9* (P) 250 250 PJ: 9-12+92 = 4 Demand 300 200 250 450 1,200* the "most negative index" We focus on cell PT (index = -9). Its closed path is: PT to PB to YB to YT, and back to PT. To increase the quantity in PT, we need to adjust PB down, YB up, and YT down. Therefore, the next improved plan is: Valley (V) $6 300 $3 Junction (J) $7 Part (b) Find the indices (show steps) Supply Row M first, then rows Y and P Town (T) $8 50 $10 Burg (B) $4 FROM Macon (M) York (Y) Perry (P) Demand 350 $2 250 600 $14 $4 S9 $9 350 $12 100 450 150 200 250 1.200 300 250 Asterisk the most negative index" (show steps). Part (a) Find the new TC = Junction (J) $7 Burg (B) $4 Part (e) Find the indices (show steps) Supply Row M first, then rows Y and P 350 S2 $9 Part (0) Determine the next improved plan. To Valley Town FROM (T) Macon $6 $8 (M) York $3 $10 (Y) Perry $14 $4 (P) Demand 300 200 Part (d) Find the new TC = Part (f) Is the current solution optimal? 600 $9 $12 250 1.200 250 450 Asterisk the "most negative index" (show steps). Explain (hint: see Online Module 8, p.M8-4)