4. (22 points) A small machine shop has five existing machines (M1 through M5) located at coordinate locations P1=(20,20),P2=(10,25),P3=(10,20),P4=(30,15), and P5= (15,10), respectively. Two new machines (N1 and N2 ) are to be located in the shop. It is anticipated that there will be ten trips per day between the new machines. The number of trips per day between each existing machine and the new machine is given in the table below. a) Formulate the objective function assuming that rectilinear distance is used (6 points). b) Formulate the objective function assuming that Euclidean distance is used ( 6 points). c) Solve the problem using squared Euclidean distances (10 points). Note: The objective functions should be written in open form for full credit in parts a and b