8. a. 50 Boston 100 Dever 70 Dallas 20 17 100 2 12 Atlanta 10 Los 60 Angeles 13

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.5: Facility Location Models
Problem 27P
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Please only anser part b & show steps to computing the optimal solution using excel solver.

8. a.
|50
Boston
100
Denver
13
2
Dallas
| 70
20
17
100 Allanta
12
10
3
Los
Angeles
18
13
3
150
Chicago
16
St. Paul s0
b. There are alternative optimal solutions.
Solution 1
Solution 2
Denver to St. Paul:
10
50
50
20
Chicago to Los Angeles: 60
70
Denver to St. Paul:
10
50
Atlanta to Boston:
Atlanta to Dallas:
Atlanta to Boston:
Atlanta to Los Angeles: 50
Chicago to Dallas:
Chicago to Los Angeles: 10
Chicago to St. Paul:
Chicago to Dallas:
70
Chicago to St. Paul:
70
Total Profit: $4240
Transcribed Image Text:8. a. |50 Boston 100 Denver 13 2 Dallas | 70 20 17 100 Allanta 12 10 3 Los Angeles 18 13 3 150 Chicago 16 St. Paul s0 b. There are alternative optimal solutions. Solution 1 Solution 2 Denver to St. Paul: 10 50 50 20 Chicago to Los Angeles: 60 70 Denver to St. Paul: 10 50 Atlanta to Boston: Atlanta to Dallas: Atlanta to Boston: Atlanta to Los Angeles: 50 Chicago to Dallas: Chicago to Los Angeles: 10 Chicago to St. Paul: Chicago to Dallas: 70 Chicago to St. Paul: 70 Total Profit: $4240
8. Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced
by the lce Age Corporation. Ice Age manufactures the refrigerators at four locations around
the country: Boston, Dallas, Los Angeles, and St. Paul. Plans call for the following num-
ber (in thousands) of refrigerators to be produced at each location:
Boston
Dallas
Los Angeles
St. Paul
50
70
60
80
Forbelt's three plants are capable of producing the motors. The plants and production ca-
pacities (in thousands) are as follows:
Denver
100
Atlanta
Chicago
100
150
Because of varying production and transportation costs, the profit that Forbelt eams on
cach lot of 1000 units depends on which plant produced the lot and which destination it
was shipped to. The following table gives the accounting department estimates of the profit
per unit (shipments will be made in lots of 1000 units):
Shipped To
Produced At
Boston
Dallas
Los Angeles
St. Paul
Denver
Atlanta
8
12
13
13
10
20
17
18
Chicago
16
With profit maximization as a criterion, Forbelt's management wants to determine how
many motors should be produced at cach plant and how many motors should be shipped
from cach plant to cach destination.
a. Develop a network representation of this problem.
b Find the optimal solution.
Transcribed Image Text:8. Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced by the lce Age Corporation. Ice Age manufactures the refrigerators at four locations around the country: Boston, Dallas, Los Angeles, and St. Paul. Plans call for the following num- ber (in thousands) of refrigerators to be produced at each location: Boston Dallas Los Angeles St. Paul 50 70 60 80 Forbelt's three plants are capable of producing the motors. The plants and production ca- pacities (in thousands) are as follows: Denver 100 Atlanta Chicago 100 150 Because of varying production and transportation costs, the profit that Forbelt eams on cach lot of 1000 units depends on which plant produced the lot and which destination it was shipped to. The following table gives the accounting department estimates of the profit per unit (shipments will be made in lots of 1000 units): Shipped To Produced At Boston Dallas Los Angeles St. Paul Denver Atlanta 8 12 13 13 10 20 17 18 Chicago 16 With profit maximization as a criterion, Forbelt's management wants to determine how many motors should be produced at cach plant and how many motors should be shipped from cach plant to cach destination. a. Develop a network representation of this problem. b Find the optimal solution.
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