2. (35 pts) Four machines are located in a plant at points (0,30), (20,10), (40,50), and (50,30). These machines require maintenance at expected frequencies of 30, 12, 25, and 20 times per year, respectively. Because of the nature of the maintenance, all machines must be maintained at the maintenance center. A machine can be serviced by exactly one maintenance center. Moreover, the cost of transporting the machines to and from the maintenance center is $5 per unit of distance (the $5 per unit distance covers the cost to and from so it is the two way cost – not a one way cost), including the cost of lost profits resulting from the machines being down. The annual cost of owning and operating a maintenance center is $5000. Rectilinear travel is assumed.

Determine the optimal location if there will be one maintenance center

Determine the optimal cost if there is one maintenance center

Calculate the number of possible ways to allocate the machines across two maintenance centers

List all possible machine to maintenance center assignment combinations for two maintenance centers indicating which machines are allocated to which maintenance center.

Determine the optimal locations if there will be two maintenance centers

Determine the optimal cost if there are two maintenance centers

Which solution overall has the lowest cost?