Example 10.2: A new machine needs to be added into a maintenance department among five existing machines, which are currently located in coordinates: P1 (1, 1), P2 (6, 2), P3 (2, 8), P4 (3, 6) and P5 (8, 4). The cost per unit distance traveled between the new machine and each existing machine is the same. The number of trips per day between the new machine and the existing machines 1, 2, 3, 4 and 5 are 10, 20, 25, 20 and 25, respectively.

1) Please identify the best location for the new machine. Your submission needs to include:

% 430 HW 10 Problem 1

% Define x values for calculating the cost along the x axis

x=1:0.1:8;

% Calculate the sub-total cost along the x axis

sumx=10*abs(x-1)+20*abs(x-6)+25*abs(x-2)+20*abs(x-3)+25*abs(x-8);

% Calculate the minimum x sub-total cost and the corresponding x value

[xmin, indexx]=min(sumx);

% Figure out the x value at which the total cost along the x axis is

% minimum

xvalue=x(indexx)

xmin

% Define y values for calculating the cost along the y axis

y=1:0.1:8;

% Calculate the sub-total cost along the y axis

sumy=10*abs(y-1)+20*abs(y-2)+25*abs(y-8)+20*abs(y-6)+25*abs(y-4);

% Calculate the minimum y sub-total cost and the corresponding y value

[ymin, indexy]=min(sumy);

% Figure out the y value at which the total cost along the y axis is

% minimum

yvalue=y(indexy)

ymin

MinTotalCost=xmin+ymin

%End%

1

b) The calculated minimum cost and the location coordinates

The minimum total cost is 440 at (3, 4)