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Part (a) Find the new TC- Part (c) Determine the next improved plan. To Valley (1) FROM Madison Yonkers (1) Pittsburgh $8 $5 $15 Town (7) $10 200 $12 $6 Demand 350 Part (d) Find the new TC- Part (1) Is the current solution optimal? Junction 250 $9 $4 $11 Explain Burg (B) $6 $11 ||$14 450 Part (e) Find the indices (show steps) Supply Row M first, then rows Y and P 400 600 (show steps). 250 1,250 Asterisk the “most negative index" (show steps). (hint: see Online Module 8, p.M8-4).

Part (a) Find the new TC- Part (c) Determine the next improved plan. To Valley (1) FROM Madison Yonkers (1) Pittsburgh $8 $5 $15 Town (7) $10 200 $12 $6 Demand 350 Part (d) Find the new TC- Part (1) Is the current solution optimal? Junction 250 $9 $4 $11 Explain Burg (B) $6 $11 ||$14 450 Part (e) Find the indices (show steps) Supply Row M first, then rows Y and P 400 600 (show steps). 250 1,250 Asterisk the “most negative index" (show steps). (hint: see Online Module 8, p.M8-4).

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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(2) Find an optimal solution for the following transportation problem. To Town (7) FROM Madison (M) Yonkers (1) Pittsburgh (P) Demand FROM Madison (M) Yonkers (Y) Pittsburgh FROM Valley (1) 350 To Valley (1) To FROM Madison (M) Yonkers (Y) 350 Pittsburgh (P) Demand $8 $15 $5 350 $8 Valley (1) Using the Stepping-Stone method to find an optimal plan. Town Junction (7) (J) $5 $15 Madison (M) Yonkers (1) Pittsburgh (P) Demand 350 Part (a) Find the new TC=_ $8 50 150 350 200 250 The above feasible plan is obtained by applying the Northwest Corner Rule (e.g., 300 from M to V, etc.), and its total cost = 350($8) +50($10)+150($12) +250($4) +200($11) +250($14) = $11.800. $5 $15 $8 $5 $15 50 150 $10 Town (T) 50 $12 150 200 $6 200 $10 $12 $6 Part (c) Determine the next improved plan. To Valley Town (7) $10 $12 $6 $10 Junction $12 250 $6 350 Part (d) Find the new TC = Part (1) Is the current solution optimal? 250 $9 $11 $4 Demand 350 200 250 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: 250 250 $9 Junction (J) 250 $4 $11 $9 $4 $11 Junction $9 $4 Burg (B) Supply $6 200 $11 250 450 Explain 200 Burg (B) 250 450 $11 $14 350 100 450 $11 Burg (B) $6 $14 $11 Burg (B) $6 $14 450 $6 $11 400 $14 600 250 1,250 Supply (row M first, then rows Y and P) MJ: 9-4+12-10-7 400 600 250 1,250 400 Part (b) Find the indices (show steps) Supply Row M first, then rows Y and P 600 The improvement indices below are determined as follows: 250 1,250 MB: 6−11+12–10 =-3 YV: 5-12+10-8-5 PV: 15−14+11−12+10-8-2 PT: 6-14+11-12--9 PJ: 11-14+11-4-4 * the "most negative index" 400 600 Part (e) Find the indices (show steps) Supply Row M first, then rows Y and P Asterisk the "most negative index" (show steps). 250 1,250 Asterisk the "most negative index" (show steps). (hint: see Online Module 8, p.M8-4).
Transcribed Image Text:(2) Find an optimal solution for the following transportation problem. To Town (7) FROM Madison (M) Yonkers (1) Pittsburgh (P) Demand FROM Madison (M) Yonkers (Y) Pittsburgh FROM Valley (1) 350 To Valley (1) To FROM Madison (M) Yonkers (Y) 350 Pittsburgh (P) Demand $8 $15 $5 350 $8 Valley (1) Using the Stepping-Stone method to find an optimal plan. Town Junction (7) (J) $5 $15 Madison (M) Yonkers (1) Pittsburgh (P) Demand 350 Part (a) Find the new TC=_ $8 50 150 350 200 250 The above feasible plan is obtained by applying the Northwest Corner Rule (e.g., 300 from M to V, etc.), and its total cost = 350($8) +50($10)+150($12) +250($4) +200($11) +250($14) = $11.800. $5 $15 $8 $5 $15 50 150 $10 Town (T) 50 $12 150 200 $6 200 $10 $12 $6 Part (c) Determine the next improved plan. To Valley Town (7) $10 $12 $6 $10 Junction $12 250 $6 350 Part (d) Find the new TC = Part (1) Is the current solution optimal? 250 $9 $11 $4 Demand 350 200 250 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: 250 250 $9 Junction (J) 250 $4 $11 $9 $4 $11 Junction $9 $4 Burg (B) Supply $6 200 $11 250 450 Explain 200 Burg (B) 250 450 $11 $14 350 100 450 $11 Burg (B) $6 $14 $11 Burg (B) $6 $14 450 $6 $11 400 $14 600 250 1,250 Supply (row M first, then rows Y and P) MJ: 9-4+12-10-7 400 600 250 1,250 400 Part (b) Find the indices (show steps) Supply Row M first, then rows Y and P 600 The improvement indices below are determined as follows: 250 1,250 MB: 6−11+12–10 =-3 YV: 5-12+10-8-5 PV: 15−14+11−12+10-8-2 PT: 6-14+11-12--9 PJ: 11-14+11-4-4 * the "most negative index" 400 600 Part (e) Find the indices (show steps) Supply Row M first, then rows Y and P Asterisk the "most negative index" (show steps). 250 1,250 Asterisk the "most negative index" (show steps). (hint: see Online Module 8, p.M8-4).
Expert Solution
Step 1 Introduction:-

The transportation model is used to calculate the minimum cost of the route by selecting different supplies and demands. There are basically the main methods that are used under the transportation model, i.e., the least cost method, VAM, and northwest corners. These methods help in finding the feasibility of the solution but optimally of the solution can be checked the other methods: - The steppingstone method, MODI method, or linear programming method.

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