Satco Foods produces tomato sauce at three plants located in

Satco Foods produces tomato sauce at three plants located in Los Angeles, New York and St. Louis.  The monthly production capacity (in millions of pounds) of each plant and variable production cost (per pound) are as follows:


Production Capacity               Variable Production Cost       

Plant                           (in millions)                                   (per pound)

New York                         9                                                     $.20

Los Angeles                      7                                                     $.23          

St. Louis                            8                                                     $.18


After the tomato sauce is produced it is shipped to four different warehouses located in Philadelphia, Chicago, Atlanta and Kansas City. The shipping cost from plant to warehouse is the same for all locations it is $.0002 pounds per mile.   At least 2,000,000 pounds of tomato sauce per year must be shipped through a warehouse for it to be economical to use.  If a warehouse site is not used it incurs no cost.  To get some idea of monthly shipping and operating cost at the warehouses, Satco has tabulated historical data in file Satco_Template.xlsx.  This file contains information of monthly shipping and operating cost for the warehouses.  It is based on analysis of other similar products that are stored in the warehouse and shipped to final destinations.  This data is provided in two tables.  Table 1 shows shipping/ transportation cost from the warehouses to final destinations as a function of pounds and mileage shipped.  Table 2 shows average warehouse operating costs for the warehouse operations over the last 18 months.  These operating costs are associated with storage and handling of product on a per pound basis.  The cost are segregated by east coast operations (average for Philadelphia and Atlanta warehouses) and mid west operations (average for Chicago and Kansas City Operations).  Use this information to determine unit shipping / transportation and operation cost associated with the warehouses.

Satco ships tomato sauce to six distributors from the warehouse operations.  The monthly amounts of tomato sauce required by each distributor is as follows:

                                                      Monthly Requirement

Distributor            Location          (in millions of pounds)           

1                      Boston                         2

2                      Memphis                     2.5

3                      Detroit                         4

4                      Denver                        2

5                      Dallas                          3.5

6                      San Francisco             5

The travel distance (in miles) between each plant and potential warehouse site is as follows:

Philadelphia Chicago Atlanta Kansas City

New York 100 802 841 1198

Los Angles 2706 2054 2182 257

St. Louis 868 289 541 257

The travel distance (in miles) between each warehouse and each distributor is as follows:

Mileage Data from Warehouse to Demand Destination

Boston Memphis Detroit Denver Dallas San Franciso

Philadelphia 296 1000 576 1691 1452 2866

Chicago 963 530 266 996 917 2142

Atlanta 1037 371 699 1398 795 2496

Kansas City 1391 451 743 600 489 1835

Determine how Satco can minimize the next month cost of getting tomato sauce from plants to customers.  Hint: use the historical data in tables to forecast to help solve the transportation problem.

TABLE 1: Warehouse Shipping Cost DataTABLE 2 - Operating Cost ($/LB) History for Warehouses
POUNDS SHIPPEDMILES SHIPPEDTotal COSTEast Coat Ops     Phila & AtlMid West Ops       Chi & KC
40000300$13,889.54MonthCost / lbMonthCost / lb
48000400$19,296.1010.0210.014
56000500$25,289.9420.01520.015
64000380$25,094.4930.02330.016
72000420$29,323.6640.02440.015
80000590$38,688.3650.1850.016
88000780$49,111.9460.02560.017
96000990$60,853.7670.02670.016
1040001000$65,554.6580.02680.017
112000350$42,187.9890.02990.019
120000450$51,092.73100.028100.02
128000562$60,937.77110.029110.02
136000782$75,748.82120.03120.021
144000345$53,691.41130.03130.021
152000672$78,222.92140.029140.02
160000981$99,255.48150.032150.021
168000189$46,002.37160.032160.023
176000329$63,944.35170.033170.024
184000417$75,665.58180.034180.024
192000506$85,680.52
Mileage data from plant to warehouse
PHILCHICATLINDYKC
NY1008028417131198
LA27062054218220731589
STL868289541235257
Mileage data from warehouse to demand destination
BOSTMEMPDETDENVDALLSF
PHIL2961000576169114522866
CHIC9635302669969172142
ATL103737169913987952496
KC13914517436004891853