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The calculated minimum cost and the location coordinates

The calculated minimum cost and the location coordinates

1. Example 10.1: 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. (50 pts)

1) Please 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. Please 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. Please 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).

2. There are six Walmart stores in Eastern Kentucky. Their coordinates are identified (in mile): P1 (60, 180), P2 (150, 250), P3 (5, 90), P4 (210, 120), P5 (70, 10), and P6 (170, 50). A new distribution center is planned to supply merchandise to these six stores. The cost per unit distance traveled between the distribution center and each store is the same. The number of freight truck trips per week between the distribution center and the store 1, 2, 3, 4, 5 and 6 are expected to be 20, 10, 50, 60, 25 and 30, respectively. (50 pts)

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

a) The m-file

b) The calculated minimum cost and the location coordinates

2) The best place identified in 1) is unfortunately located in middle of the Cave Run Lake. Thus, an iso-cost contour map is needed to figure out possible alternative locations. Please 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. Please mark the identified best location, P1, P2, P3, P4, P5, and P6 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).

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MSU, Qingzhou Xu

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