Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The fol- lowing table shows the shipping costs per truckload ($100s), supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago. To From New York Philadelphia Chicago Boston Supply $ 9 $ 12 Tampa Miami $ 14 $ 17 200 11 10 6. 10 200 Fresno 12 8 15 7 200 Demand 130 170 100 150 a. Set up the transportation tableau for this problem and determine the initial solution using the minimum cell cost method. b. Solve using MODI. c. Are there multiple optimal solutions? Explain. If so, identify them.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These
warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The fol-
lowing table shows the shipping costs per truckload ($100s), supply, and demand. Because of an
agreement between distributors, shipments are prohibited from Miami to Chicago.
To
From
New York
Philadelphia
Chicago
Boston
Supply
Tampa
$ 9
$ 14
$ 12
$ 17
200
Miami
11
10
6
10
200
Fresno
12
8
15
7
200
Demand
130
170
100
150
a. Set up the transportation tableau for this problem and determine the initial solution using the
minimum cell cost method.
b. Solve using MODI.
c. Are there multiple optimal solutions? Explain. If so, identify them.
d. Formulate this problem as a linear programming model.
Transcribed Image Text:Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The fol- lowing table shows the shipping costs per truckload ($100s), supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago. To From New York Philadelphia Chicago Boston Supply Tampa $ 9 $ 14 $ 12 $ 17 200 Miami 11 10 6 10 200 Fresno 12 8 15 7 200 Demand 130 170 100 150 a. Set up the transportation tableau for this problem and determine the initial solution using the minimum cell cost method. b. Solve using MODI. c. Are there multiple optimal solutions? Explain. If so, identify them. d. Formulate this problem as a linear programming model.
Coal is mined and processed at the following four mines in Kentucky, West Virginia, and Virginia.
Location
Сараcity (tons)
A. Cabin Creek
90
B. Surry
C. Old Fort
D. McCoy
50
80
60
280
These mines supply the following amount of coal to utility power plants in three cities.
Plant
Demand (tons)
1. Richmond
2. Winston-Salem
3. Durham
120
100
110
330
The railroad shipping costs ($1,000s) per ton of coal are shown in the following table. Because of
railroad construction, shipments are now prohibited from Cabin Creek to Richmond.
To
From
2
3
A
$ 7
$10
$ 5
B
12
4
C
7
3
11
D
9
5
7
a. Set up the transportation tableau for this problem, determine the initial solution using VAM,
and compute total cost.
b. Solve using MODI.
c. Are there multiple optimal solutions? Explain, If there are alternative solutions, identify them.
d. Formulate this problem as a linear programming model.
%24
Transcribed Image Text:Coal is mined and processed at the following four mines in Kentucky, West Virginia, and Virginia. Location Сараcity (tons) A. Cabin Creek 90 B. Surry C. Old Fort D. McCoy 50 80 60 280 These mines supply the following amount of coal to utility power plants in three cities. Plant Demand (tons) 1. Richmond 2. Winston-Salem 3. Durham 120 100 110 330 The railroad shipping costs ($1,000s) per ton of coal are shown in the following table. Because of railroad construction, shipments are now prohibited from Cabin Creek to Richmond. To From 2 3 A $ 7 $10 $ 5 B 12 4 C 7 3 11 D 9 5 7 a. Set up the transportation tableau for this problem, determine the initial solution using VAM, and compute total cost. b. Solve using MODI. c. Are there multiple optimal solutions? Explain, If there are alternative solutions, identify them. d. Formulate this problem as a linear programming model. %24
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