The town of Lexington purchases gasoline from three vendors to fuel its fleet of municipal vehicles. Each vendor delivers gasoline in 6,000 gallon quantities. Since vendors must deliver the fuel, a transportation fee (based on the distance the vendor must travel) is added to each delivery. The number of deliveries required by each location, the cost of supplying a truckload of gasoline to each location from each vendor, and the number of truckloads each vendor can deliver are provided below: PoliceStation FireStation BusDepot PublicWorksGarage Deliveries(truckloads)available Vendor A Vendor B Vendor C Deliveries(truckloads)required $500 $350 $400 12 $525 $425 $375 2 $550 $450 $625 18 $600 $575 $475 6 20 14 10 Assuming that the price per gallon of fuel is the same for each vendor, develop a linear programming model that minimizes the total transportation fee that Lexington must pay for supplying all of its facilities’ fuel needs.
The town of Lexington purchases gasoline from three vendors to fuel its fleet of municipal vehicles. Each vendor delivers gasoline in 6,000 gallon quantities. Since vendors must deliver the fuel, a transportation fee (based on the distance the vendor must travel) is added to each delivery. The number of deliveries required by each location, the cost of supplying a truckload of gasoline to each location from each vendor, and the number of truckloads each vendor can deliver are provided below:
| Police Station |
Fire Station |
Bus Depot |
Public Works Garage |
Deliveries (truckloads) available |
|
|
Vendor A Vendor B Vendor C Deliveries |
$500 $350 $400 12
|
$525 $425 $375 2
|
$550 $450 $625 18
|
$600 $575 $475 6
|
20 14 10
|
Assuming that the price per gallon of fuel is the same for each vendor, develop a linear programming model that minimizes the total transportation fee that Lexington must pay for supplying all of its facilities’ fuel needs.
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