The Road net 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 warehouse 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 truckload shipment from each warehouse to each terminal. The profits differ as a result of difference in product shipped, shipping costs and transfer rates:
|
|
Terminal
|
|
Warehouse
|
St Louis
|
Atlanta
|
New York
|
|
Charlotte
|
$1,800
|
$100
|
$1,600
|
|
Memphis
|
1000
|
700
|
900
|
|
Louisville.
|
1400
|
800
|
2200
|
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.