AlaCom, a manufacturer of motherboards for personal computers, is opening a new manufacturing plant in Birmingham, Alabama. Once the boards have been manufactured at various areas in the plant, they...

AlaCom, a manufacturer of motherboards for personal computers, is opening a new manufacturing plant in Birmingham, Alabama. Once the boards have been manufactured at various areas in the plant, they will be transported to a packaging area, using an overhead conveyor belt system. A line in the system will be installed from each of the four production areas to a central switching station. From the switching station, the products will be rerouted along the main conveyor belt to the packaging area. Given the location of air conditioning, ventilation, and lighting systems in the plant, there are many possible configurations for the design of the conveyor belt system from the switching station to the packaging area as shown in the figure for problem 27. Distances are in feet.

Each leg of the system will consist of two conveyor belts, one going in each direction. It will cost AlaCom $100 per linear foot to install the conveyor belt in each direction. Additional costs include $18,000 for each start station at the production area, $20,000 for the finish station at the packaging area, and $52,000 for the switching station. Given the possible choices for constructing the conveyor belt system, what is the minimum-cost conveyor belt system AlaCom can install?