Transportation Problems

1. Green Valley Mills produces carpet at plants in St. Louis and Richmond. The carpet is then shipped to two outlets, located in Chicago and Atlanta. The cost per ton of shipping carpet from each of the two plants to the two warehouses is as follows:

To (cost)
From Chicago Atlanta
St. Louis $40 $65
Richmond 70 30
The plant at St. Louis can supply 250 tons of carpet per week; the plant at Richmond can supply 400 tons per week. The Chicago outlet has a demand of 300 tons per week, and the outlet at Atlanta demands 350 tons per week. The company wants to know the number of tons of carpet to ship from each plant to each outlet to minimize the total shipping cost. Solve this transportation problem.

3. Given a transportation problem with the following costs, supply, and demand, find the optimal solution by using the computer:

To (cost)
From 1 2 3 Supply
A $6 $7 $4 100
B 5 3 6 180
C 8 5 7 200
Demand 135 175 170

9. Coal is mined and processed at the following four mines in Kentucky, West Virginia, and Virginia:
Location Capacity (tons)
A. Cabin Creek 90
B. Surry 50
C. Old Fort 80
D. McCoy 60
These mines supply the following amount of coal to utility power plants in three cities:

Plant Demand (tons)
1. Richmond 120
2. Winston-Salem 100
3. Durham 110

The railroads shipping costs (in thousands of dollars) per ton of coal are shown in the following table. Because of railroads construction, shipments are pro from cabin creek to Richmond:
To(coats, in $1000s)
From 1 2 3
A $7 10 5
B 12 9 4
C 7 3 11
D 9 5 7

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