Juice, Inc. produces and sells cranberry juice nationwide. They currently have five processing plants located around the country where cranberries are squashed and made into juice. These processing plants are located in the following five major cities: Los Angeles (LA), St. Paul (SP), Boston (B), Atlanta (A), and Dallas (D). Based on their plant technology, 1 ton of cranberries produces 75 gallons of cranberry juice.
Crancoop Inc. is a large cranberry cooperative that sells bulk cranberries to Juice, Inc. They have four large transfer stations located in the North (NOR), South (SOU), East (EAS), and Western (WES) United States. These transfer stations are where all the cranberries from each region's farms are stored, and they represent the supply sources for each processing plant.
After processing the raw cranberries into juice, Juice, Inc. ships the juice to four cold storage facilities in the nation, where supermarkets get their supply of cranberry juice. The cold storage facilities are located in California (CAL), Minnesota (MN), New York (NY), and Florida (FL).
You have been hired as a consultant to determine the most efficient raw product-final product distribution network for Juice, Inc. You have been given the fol- lowing unit transportation costs, supply capacities, and demand levels:
Cranberries: ($/ton of bulk cranberries)
From/To LA SP B A D Supply
($/ton) (tons)
|
NOR
|
500
|
75
|
80
|
650
|
700
|
900
|
|
SOU
|
450
|
455
|
666
|
150
|
100
|
100
|
|
EAS
|
1,000
|
225
|
50
|
100
|
950
|
500
|
|
WES
|
120
|
350
|
1,100
|
1,150
|
450
|
700
|
Cranberry Juice ($/gallon of cranberry juice)
From/To CAL MN NY FL
|
LA
|
0.10
|
1.00
|
3.00
|
3.50
|
|
SP
|
1.00
|
0.05
|
1.25
|
2.35
|
|
B
|
2.50
|
0.75
|
0.35
|
1.45
|
|
A
|
3.00
|
1.10
|
0.80
|
0.55
|
|
D
|
0.90
|
1.05
|
2.00
|
0.95
|
|
Demand
|
60,000
|
20,000
|
40,000
|
30,000
|
a. Assuming the processing plants can handle unlimited amounts of cranberries, for- mulate an LP model that minimizes total distribution costs for transporting cran- berries to the plants and cranberry juice to the cold storage facilities. Show either the LP tableau, or mathematical representation of the model.
b. Using Solver, solve the problem in part a.
c. Write a summary of the optimal solution.
d. Write a summary of your sensitivity analysis with respect to objective function coefficients.