12. Major Motors produces its Trans National model in three plants located in Flint, Michigan; Fresno, California; and Monterrey, Mexico. Dealers receive cars from regional distribution centers located in Phoenix, Arizona; Davenport, Iowa; and Columbia, South Carolina. Anticipated production at the plants over the next month (in 100s of cars) is 43 at Flint, 26 at Fresno, and 31 at Monterrey. Based on firm orders and other requests from dealers, Major Motors has decided that it needs to have the following numbers of cars at the regional distribution centers at month's end: Phoenix, 26; Davenport, 28; and Columbia, 30. Suppose that the cost of shipping 100 cars from each plant to each distribution center is given in the following matrix (in $1,000s): то Phoenix Davenport Columbia F Flint 12 8 17 R Fresno 7 14 21 Monterrey 18 22 31 м a. Convert the problem to a balanced problem by adding an appropriate row or column and find the optimal solution using Solver. b. Now find the optimal solution using Solver and inequality constraints. c. Do the solutions in (a) and (b) match? Why or why not? d. Suppose that the route between Monterrey and Columbia is no longer available due to a landslide on a key road in Mexico. Modify the model in (b) and resolve to find the optimal solution. Has the objective value increased or decreased? Explain why.
12. Major Motors produces its Trans National model in three plants located in Flint, Michigan; Fresno, California; and Monterrey, Mexico. Dealers receive cars from regional distribution centers located in Phoenix, Arizona; Davenport, Iowa; and Columbia, South Carolina. Anticipated production at the plants over the next month (in 100s of cars) is 43 at Flint, 26 at Fresno, and 31 at Monterrey. Based on firm orders and other requests from dealers, Major Motors has decided that it needs to have the following numbers of cars at the regional distribution centers at month's end: Phoenix, 26; Davenport, 28; and Columbia, 30. Suppose that the cost of shipping 100 cars from each plant to each distribution center is given in the following matrix (in $1,000s): то Phoenix Davenport Columbia F Flint 12 8 17 R Fresno 7 14 21 Monterrey 18 22 31 м a. Convert the problem to a balanced problem by adding an appropriate row or column and find the optimal solution using Solver. b. Now find the optimal solution using Solver and inequality constraints. c. Do the solutions in (a) and (b) match? Why or why not? d. Suppose that the route between Monterrey and Columbia is no longer available due to a landslide on a key road in Mexico. Modify the model in (b) and resolve to find the optimal solution. Has the objective value increased or decreased? Explain why.
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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Transcribed Image Text:12. Major Motors produces its Trans National model in three plants located in Flint,
Michigan; Fresno, California; and Monterrey, Mexico. Dealers receive cars from
regional distribution centers located in Phoenix, Arizona; Davenport, Iowa; and
Columbia, South Carolina. Anticipated production at the plants over the next
month (in 100s of cars) is 43 at Flint, 26 at Fresno, and 31 at Monterrey. Based on
firm orders and other requests from dealers, Major Motors has decided that it
needs to have the following numbers of cars at the regional distribution centers
at month's end: Phoenix, 26; Davenport, 28; and Columbia, 30. Suppose that the
cost of shipping 100 cars from each plant to each distribution center is given in the
following matrix (in $1,000s):
то
Phoenix
Davenport
Columbia
F
Flint
12
8
17
R
Fresno
7
14
21
Monterrey
18
22
31
м
a. Convert the problem to a balanced problem by adding an appropriate row or
column and find the optimal solution using Solver.
b. Now find the optimal solution using Solver and inequality constraints.
c. Do the solutions in (a) and (b) match? Why or why not?
d. Suppose that the route between Monterrey and Columbia is no longer available due
to a landslide on a key road in Mexico. Modify the model in (b) and resolve to find
the optimal solution. Has the objective value increased or decreased? Explain why.
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