Q. Distributing a Product The Lincoln Lock Company manufactures a commercial security lock at plants in Atlanta, Louisville, Detroit, also Phoenix. The unit cost of production at each plant is $35.50, $37.50, $37.25, also $36.25, also the annual capacities are 18,000, 15,000, 25,000, also 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 Elucidate how in the following table, along with the forecasted demand from each distributor for the coming year.

Open table as spreadsheet

Tacoma Sandi ego Dallas Denver St Louis Tampa Baltimore

Atlanta 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 5.500 11.500 10.500 9.600 15.400 12.500 6.600

a. Determine the least costly way of shipping locks from plants to distributors.

b. Elucidate how the network diagram corresponding to the solution in (a). That is, label each of the arcs in the solution also verifies that the flows are consistent with the given information.

c. Assume that the unit cost at each plant were $10 higher than the original figure. Illustrate change in the optimal distribution plan would result? Illustrate general conclusions can you draw for transportation models with no identical plant-correlated costs?