Anew 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. (50 pts)

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

a) the m-file
b) the calculated minimum cost and the location coordinates

2) alternatives are required for the best location of 1). thus, an iso-cost contour map is needed to identify possible alternative locations. calculate the iso-cost contour map of this question. your submission needs to include:

a) the m-file.
b) a large-area, coarse map with labels. mark the identified best location, p1, p2, p3, p4, and p5 on this contour map.
c) a small-area (zoom in on the center), fine map without labels.

3) compare 1) and 2)’s results and check if the coordinate location in 1) matches the center of the contour lines in 2)