The Lannon 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, respectively; the annual capacities 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 demand forecast from each distributor for the coming year:

a. Determine the least costly way of producing and shipping locks from plants to distributors.
b. Suppose that the unit cost at each plant were $10 higher than the original figure. What change in the optimal distribution plan would result? What general conclusions can you draw for transportation models with nonidentical plant-related costs?