The Roadnet Transport Company has expanded its shipping capacity by purchasing 90 trailer trucks from a bankrupt competitor. The company subsequently located 30 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of these warehouses to terminals in St. Louis, Atlanta, and New York. Each truck is capable of making one shipment per week. The terminal managers have each indicated their capacity for extra shipments. The manager at St. Louis can accommodate 40 additional trucks per week, the manager at Atlanta can accommodate 60 additional trucks, and the manager at New York can accommodate 50 additional trucks. The company makes the following profit per truck-load shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport rates: Terminal Warehouse St. Louis Atlanta New York Charlotte $1,800 $2,100 $1,600 Memphis 1,000 700 900 Louisville 1,400 800 2,200 The company wants to know how many trucks to assign to each route (i.e., warehouse to terminal) to maximize profit. 1. Formulate a linear programming model for this problem. 2. Solve the model by using the computer.
The Roadnet Transport Company has expanded its shipping capacity by purchasing 90 trailer trucks from a bankrupt competitor. The company
subsequently located 30 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes
shipments from each of these warehouses to terminals in St. Louis, Atlanta, and New York. Each truck is capable of making one shipment per
week. The terminal managers have each indicated their capacity for extra shipments. The manager at St. Louis can accommodate 40 additional
trucks per week, the manager at Atlanta can accommodate 60 additional trucks, and the manager at New York can accommodate 50 additional
trucks. The company makes the following profit per truck-load shipment from each warehouse to each terminal. The profits differ as a result of
differences in products shipped, shipping costs, and transport rates:
Terminal
Warehouse St. Louis Atlanta New York
Charlotte $1,800 $2,100 $1,600
Memphis 1,000 700 900
Louisville 1,400 800 2,200
The company wants to know how many trucks to assign to each route (i.e., warehouse to terminal) to maximize profit.
1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer.
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