The Roadnet Transport Company expanded its shipping capacity

The Roadnet Transport Company 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 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 truckload shipment from each warehouse to each
terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport
rates:

The company wants to know how many trucks to assign to each route (i.e., warehouse to terminal) to
maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.

Solution