3.4 Distributing a Product: The Lincoln Lock Company manufactures a commercial security lock at plants in Atlanta, Louisville, Detroit, and Phoenix. The unit cost of production at each plant is 35.50, 37.50, 37.25, and $36.25, and the annual capac- ities are 18,000, 15,000, 25,000, and 20,000, respectively. The locks are sold through wholesale distributors in seven locations around the country. The unit shipping cost for each plant-distributor combination is shown in the following table, along with the forecasted demand from each distributor for the coming year. in Atlanta Tacoma San Diego Dallas Denver St. Louis Tampa Baltimore 2.50 2.75 1.75 2.00 2.10 1.80 1.65 Louisville 1.85 1.90 1.50 1.60 1.00 1.90 1.85 Detroit 2.30 2.25 1.85 1.25 1.50 2.25 2.00 Phoenix 1.90 0.90 1.60 1.75 2.00 2.50 2.65 Demand 5500 11,500 10,500 9,600 15,400 12,500 6600 (a) Determine the least costly way of shipping locks from plants to distributors. (b) Show the network diagram corresponding to the solution in (a). That is, label each of the arcs in the solution and verify that the flows are consistent with the given information.

Fig: 1