A factory that is located 20 km from a railway would like to reduce the rransportation costs by building a new road to the rail line. This will, however, increase the road transprotation costs to the railroad, but reduce the railroad costs. Where should the new rail link, D be located so that the transportation costs are the minimum.

What is known:

• The length of the old railway, AB, is 100 km.
• The old road distance from the factory to the railway is 20 km as shown in the diagram.
• The cost to ship by rail verses road is 3 to 5.

Where should the rai link, D, be built so that the transportation costs are the lowest?

• The total transportation cost is the sum of the railroad and road costs.
• The minimum transportation cost may occur when the rail link, D, is located at A, B or somewhere between A and B.