Question

Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers​ (located in cities​ A, B, and​ C). As shown in the table​ below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following​ information Location Deliveries per day x-coordinate y-coordinate A 9 100 100 B 8 400 200 C 7 300 400 Which of these three locations yields the smallest total travel​ distance, based on Euclidean​ distances?

Answer 1

Euclidean distance:

Distance Between A and B => sqrt((100-400)^2+(100-200)^2) = 316.227766

Distance Between A and C => sqrt((100-300)^2+(100-400)^2) = 360.5551275

Distance Between B and C => sqrt((400-300)^2+(200-400)^2) = 223.6067977

Location A:

For A to A, Total travel distance = Deliveries per day * Distance between A and A = 0
For A to B, Total travel distance = Deliveries per day * Distance between A and B = 8*316.227766 = 2529.822128

For A to C, Total travel distance = Deliveries per day * Distance between A and C = 7*360.5551275 = 2523.885893

Total distance traveled = 0+2529.822128+2523.885893 = 5053.708021

Location B

For B to A, Total travel distance = Deliveries per day * Distance between B and A = 9*316.227766 = 2846.049894
For B to B, Total travel distance = Deliveries per day * Distance between B and B = 0

For B to C, Total travel distance = Deliveries per day * Distance between B and C = 7*223.6067977 = 1565.247584

Total distance traveled = 2846.049894+0+1565.247584 = 4411.297478

Location C

For C to A, Total travel distance = Deliveries per day * Distance between C and A = 9*360.5551275 = 3244.996148
For C to B, Total travel distance = Deliveries per day * Distance between C and B = 8*223.6067977 = 1788.854382

For C to C, Total travel distance = Deliveries per day * Distance between C and C = 0

Total distance traveled = 3244.996148+1788.854382+0 = 5033.85053

Location B yields the smallest total travel​ distance, based on Euclidean​ distances