Problem 2 An army division has five troope location(s) for supply depot(s) to se
ID: 3273567 • Letter: P
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Problem 2 An army division has five troope location(s) for supply depot(s) to serve the cam ps. The (x,y) coordinates (in miles) of the camps, A, B, C, D, and E, and the monthly number of truck trips from a supply depot to each camp are as follows: s in the desert, and the division leaders want to determine Camp 100 210 250 300 400 Monthly trip frequency 15 12 20 25 17 300 180 150 200 Consider each trip of a truck from a supply depot to a camp as a one-way trip i.e., trucks do not come back to the supply depot). The division leaders have identified 4 possible locations for supply depot(s). Each location can accommodate only one supply depot. The (x, y) coordinates of the 4 possible locations are as follows Possible location 250 220 190 300 200 230 The unit travel cost is S3 per mile and the monthly fixed cost to run each supply depot is $6,000Explanation / Answer
a) Rectilinear distance between any two points = mod(difference between X-coordinates) + mod(difference between Y-coordinates)
Considering these distances along witht the frequencies/month, we get:
Considering the costs for travel:
As 3 of the 5 minimums occur from 1, we look at which other location should be selected for A and C. We see that among the remaining locations, location number 4 is the cheapest to service the camps A and C. This is deduced by comparing the additional fixed costs because of including a new location vs how much savings can be achieved by adding a new location.
So, 2 camps should be selected, which are 1 and 4.
b) Straight Line distance between any two points = sqrt[(difference between X-coordinates)2 +(difference between Y-coordinates)2]
Considering these distances along witht the frequencies/month, we get:
Considering the costs for travel:
As 3 of the 5 minimums occur from 1, we look at which other location should be selected for A and C. We see that among the remaining locations, location number 4 is the cheapest to service the camps A and C. This is deduced by comparing the additional fixed costs because of including a new location vs how much savings can be achieved by adding a new location.
So, 2 camps should be selected, which are 1 and 4
Rectilinear Distance between points LocationCamp A B C D E 1 250 60 200 100 150 2 170 80 180 180 230 3 160 70 230 190 240 4 300 310 50 250 300Related Questions
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