Three plants are to be located at points

X1=(x1,y1), X2=(x2,y2), and X3=(x3,y3). 

There are five customers currently located at the points 

P1=(3,15), P2=(25,45), P3=(45,54), P4=(15,53), and P5=(45,15). 

The shipment of products from the plants to customers per month, measured in truckloads, are 90, 110, 150, 75, and 175 truckloads, respectively. The cost of transporting a truckload of product from the plants to customers is $1 per unit distance. Assume the capacity of each plant is 200 truckloads of product, a customer is served by only one plant, no interaction between any two plants and rectilinear distance measure between plants and customers. Formulate the problem as a mixed integer linear program and solve.