The Sentry Lock Corporation manufactures a popular commercial security lock at plants in Macon, Louisville, Detroit, and Phoenix. The per unit cost of production at each plant is $35.50, $37.50, $39.00, and $36.25, respectively, and the annual production capacity at each plant is 18,000, 15,000, 25,000, and 20,000, respectively. Sentry’s locks are sold to retailers through wholesale distributors in seven cities across the United States. The unit cost of shipping from each plant to each distributor is summarized in the following table along with the forecasted demand from each distributor for the coming year.

Sentry wants to determine the least expensive way of manufacturing and shipping locks from their plants to the distributors. Because the total demand from distributors exceeds the total production capacity for all the plants, Sentry realizes it will not be able to satisfy all the demand for its product, but wants to make sure each distributor will have the opportunity to fill at least 80% of the orders they receive.
a. Create a spreadsheet model for this problem and solve it.
b. What is the optimalsolution?

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Unit Shipping Cost to Distributor in Plants Tacoma San Diego Dallas Denver St. Louis Tapa Baltimore Maconte$1.85 Detroit $2.75 $1.75 .00 $.10 $1.80 $1.65 Louisville $1.85 $1.90 $1.50 $1.60 $1.00 $1.90 $1.85 $2.25 $1.85 $1.25 $1.50 $2.25 $2.00 $0.90 $1.60 $1.75 $2.00 $2.50 $2.65 $2.50 $2.30 $1.90 Phoenx Demand8,500 14,500 13,500 12,600 18,000 15,000 9,000