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
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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Question
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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