The Cross-Canada Trucking Company has expanded its shipping capacity by purchasing 120 trucks and trailers from a competitor that went bankrupt. The company subsequently located 40 of the purchased trucks at each of its shipping warehouses in Quebec City, Sault Ste. Marie, and Edmonton. The company makes shipments from each of these warehouses to terminals in Montreal, Toronto, and Calgary. Each truck is capable of making one shipment per week. The terminal managers have each indicated their capacity for extra shipments. The manager at Montreal can accommodate 40 additional trucks per week, the manager at Toronto can accommodate 60 additional trucks, and the manager at Calgary 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. Formulate a linear programming model for this problem and solve it.

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Terminal Toronto Calgary Warehouse Quebec City Sault Ste. Marie Montreal $1800 $1600 $2100 900 1000 700 2200 Edmonton 1400 800