Reference no: EM13879202

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.