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 Data				TABLE 2 - Operating Cost ($/LB) History for Warehouses
POUNDS SHIPPED	MILES SHIPPED	Total COST		East Coat Ops     Phila & Atl		Mid West Ops       Chi & KC
40000	300	$13,889.54		Month	Cost / lb	Month	Cost / lb
48000	400	$19,296.10		1	0.02	1	0.014
56000	500	$25,289.94		2	0.015	2	0.015
64000	380	$25,094.49		3	0.023	3	0.016
72000	420	$29,323.66		4	0.024	4	0.015
80000	590	$38,688.36		5	0.18	5	0.016
88000	780	$49,111.94		6	0.025	6	0.017
96000	990	$60,853.76		7	0.026	7	0.016
104000	1000	$65,554.65		8	0.026	8	0.017
112000	350	$42,187.98		9	0.029	9	0.019
120000	450	$51,092.73		10	0.028	10	0.02
128000	562	$60,937.77		11	0.029	11	0.02
136000	782	$75,748.82		12	0.03	12	0.021
144000	345	$53,691.41		13	0.03	13	0.021
152000	672	$78,222.92		14	0.029	14	0.02
160000	981	$99,255.48		15	0.032	15	0.021
168000	189	$46,002.37		16	0.032	16	0.023
176000	329	$63,944.35		17	0.033	17	0.024
184000	417	$75,665.58		18	0.034	18	0.024
192000	506	$85,680.52
Mileage data from plant to warehouse
	PHIL	CHIC	ATL	INDY	KC
NY	100	802	841	713	1198
LA	2706	2054	2182	2073	1589
STL	868	289	541	235	257
Mileage data from warehouse to demand destination
	BOST	MEMP	DET	DENV	DALL	SF
PHIL	296	1000	576	1691	1452	2866
CHIC	963	530	266	996	917	2142
ATL	1037	371	699	1398	795	2496
KC	1391	451	743	600	489	1853