(2) Find an optimal solution for the following transportation problem.TownJunction BuryFROMMadison(M)Yonkers(1)PittsburghDemand350200The above feasible plan is obtained by applying the Northwest Corner Rule (e.g., 300 from M to V, etc.), andits total cost = 350($8) +50($10)+150(512) +250(54)+200($11)+250($14) = $11.800To Valley(5)350FROMMadison(M)Yonkers(5)To Valley(5Pittsburgh(P)DemandFROMMadison(M)Yonkers350Madison$15Yonkers$8$5Using the Stepping-Stone method to find an optimal plan.TownJunctionBurgPittsburgh(P)Demand350$8$5$15Valley(1)PittsburghDemand350Part (a) Find the new TC=$8$5$1550150$8$5SIS50150$1050Town(7)150200$6$10$12Part (e) Determine the next improved plan.To Valley(5200$6Town(7)$10$12350200250the "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 inPT, we need to adjust PB down, YB up, and YT down. Therefore, the next improved plan is:ToJunction Burg$6250$10$12$6350Part (d) Find the new TC =Part (1) is the current solution optimal?_250250$9$4$11250$9250$11Junction20059250450Explain200250450$11350100450$6450$11$14$6$14Burg(8)Supply400600$6$11$142:501.250Supply400600 PP: 15-14+11-12+10-8=2PT: 6-14+11-12=250 PA 11-14+11-4-41.250Part (b) Find the indices (show steps)Supply Row M first, then rows Y and P400The improvement indices beloware determined as follows:row M first, then sows Y and P)MJ: 9-4+12-10-2MB: 6-11+12-10-3rv: 5-12+10-8=-56002501.250 Asterisk the "most negative index"(show steps).Part(e) Find the indices (show steps)Supply Row M first, then rows Y and P4006002501.250 Asterisk the "most negative index"_(show steps).

The transportation model is used to calculate the minimum cost of the route by selecting different…

(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).

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 100P