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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-distribulor combination is shown in the following table, along with the forecasted demand from each distributor for the coming year. Tacoma San Diego Dallas Denver St. Louis Tampa Baltimore Atlanta Louisville Detroit Phoenix Demand 2.50 1.85 2.75 1.75 2.00 1.60 2.10 1.80 I.65 1.90 1.50 1.85 1.00 1.90 1.85 2.30 2.25 1.25 1.50 2.25 2.00 1.90 0.90 1.60 1.75 2.00 2.50 15,400 12,500 2.65 5500 11,500 10,5009,600 6600 (c) 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 if the plant costs were $20 higher