American Steel, an Ohio-based steel manufacturing company, produces steel at its two steel mills located at Youngstown and Pittsburgh. The company distributes finished steel to its retail customers through the distribution network of regional and field warehouses shown below:

The network represents the shipment of finished steel from American Steel's two steel mills located at Youngstown (node 1) and Pittsburgh (node 2) to their field warehouses at Albany, Houston, Tempe, and Gary (nodes 6, 7, 8, and 9) through three regional warehouses located at Cincinnati, Kansas City, and Chicago (nodes 3, 4 and 5). Also, some field warehouses can be directly supplied from the steel mills.

Table 1, presents the minimum and maximum flow amounts of steel that may be shipped between different cities along with the cost per 1000 ton/month of shipping the steel.

Table 1 Arc Costs and Limits

From node	To node	Cost	Minimum	Maximum
Youngstown	Albany	500	-	1000
Youngstown	Cincinnati	350	-	3000
Youngstown	Kansas City	450	1000	5000
Youngstown	Chicago	375	-	5000
Pittsburgh	Cincinnati	350	-	2000
Pittsburgh	Kansas City	450	2000	3000
Pittsburgh	Chicago	400	-	4000
Pittsburgh	Gary	450	-	2000
Cincinnati	Albany	350	1000	5000
Cincinnati	Houston	550	-	6000
Kansas City	Houston	375	-	4000
Kansas City	Tempe	650	-	4000
Chicago	Tempe	600	-	2000
Chicago	Gary	120	-	4000

The current monthly demand at American Steel's four field warehouses is shown in Table 2.

Table 2 Monthly Demands

Field Warehouses	Monthly Demand
Albany, N.Y.	3000
Houston	7000
Tempe	4000
Gary	6000

The Youngstown and Pittsburgh mills can produce up to 10,000 tons and 15,000 tons of steel per month, respectively. The management wants to know the least cost monthly shipment plan.

Show the related LP to your transportation model.