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# Linear programming

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Optimization

The Sentry Lock Corporation manufactures a popular commercial security lock at plans in Macon, Louisville, Detroit, and Phoenix. The per unit cost of production at each plant is \$35.5, \$37.5, \$39, and \$36.25, respectively, while 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 7 cities across a nation. 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.

Unit Shipping Cost to Distributor in
Plants Tacoma San Diego Dallas Denver St. Louis Tampa Baltimore
Macon \$2.5 \$2.75 \$1.75 \$2.00 \$2.1 \$1.8 \$1.65
Louisville \$1.85 \$1.9 \$1.5 \$1.6 \$1.00 \$1.9 \$1.85
Detroit \$2.3 \$2.25 \$1.85 \$1.25 \$1.5 \$2.25 \$2.00
Phoenix \$1.9 \$0.9 \$1.6 \$1.75 \$2.00 \$2.5 \$2.65
Demand 8,500 14,500 13,500 12,600 18,000 15,000 9,000

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 they will not be able to satisfy all the demand for their product, but wants to make sure each distributor will have the opportunity to fill at least 80% of the orders they receive.

1.Build an appropriate Linear Programming Model for the Sentry Lock problem.

2.Solve your Linear Programming model by EXCEL. Attach a copy of your EXCEL model.

3.Give a brief description of the meaning of your Linear Programming solution.

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