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 Tables 1 & 2. 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	1589
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 Francisco
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 and help solve the transportation problem.

TABLE 1: Warehouse Shipping Cost Data
POUNDS SHIPPED	MILES SHIPPED	COST
40000	300	$13,889.54
48000	400	$19,296.10
56000	500	$25,289.94
64000	380	$25,094.49
72000	420	$29,323.66
80000	590	$38,688.36
88000	780	$49,111.94
96000	990	$60,853.76
104000	1000	$65,554.65
112000	350	$42,187.98
120000	450	$51,092.73
128000	562	$60,937.77
136000	782	$75,748.82
144000	345	$53,691.41
152000	672	$78,222.92
160000	981	$99,255.48
168000	189	$46,002.37
176000	329	$63,944.35
184000	417	$75,665.58
192000	506	$85,680.52

TABLE 2 - Operating Cost ($/LB) History for Warehouses
East Coat Ops Phila & Atl		Mid West Ops Chi & KC
Month	Cost / lb	Month	Cost / lb
1	0.015	1	0.014
2	0.016	2	0.015
3	0.016	3	0.016
4	0.018	4	0.015
5	0.019	5	0.016
6	0.02	6	0.017
7	0.02	7	0.016
8	0.022	8	0.017
9	0.023	9	0.019
10	0.023	10	0.02
11	0.024	11	0.02
12	0.026	12	0.021
13	0.026	13	0.021
14	0.027	14	0.02
15	0.028	15	0.021
16	0.029	16	0.023
17	0.029	17	0.024
18	0.03	18	0.024

Instructions for your tutor:

USING LINDO, answer needs to be optimal cost.