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# Linear programming

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The Lannon Lock Company manufactures commercial security locks 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:

Tacoma San Diego Dallas Denver St. Louis Tampa Baltimore

Atlanta 2.5 2.75 1.75 2 2.1 1.8 1.65
Louisville 1.85 1.9 1.5 1.6 1 1.9 1.85
Detroit 2.3 2.25 1.85 1.25 1.5 2.25 2
Phoenix 1.9 0.9 1.6 1.75 2 2.5 2.65

Demand 5,500 11,500 10,500 9,600 15,400 12,500 6,600

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 no identical plant related costs?