2. Consider the following map of six cities (customer locations), indicated by t
ID: 351581 • Letter: 2
Question
2. Consider the following map of six cities (customer locations), indicated by the six dark numbered points. The five light-colored points labeled A through E indicate five candidate (possible) locations for a new warehouse that will ship to each of the six cities a) Suppose that an equal amount of product is to be shipped to each city each month. Which candidate location (A, B, C, D or E)should be selected for the new warehouse? Show your working (2 points) b) Suppose that the monthly amount to be shipped to each of the cities is as follows: 800 tons to City 1; 300 tons to City 2;200 tons to City 3; 200 tons to City 4; 400 tons to City 5; and 100 tons to City 6. Given this shipping information, which candidate location should be selected for the new warehouse? Show your working (3 points)Explanation / Answer
The plot is of dimension (15 X 11)
The Coordinates of 1- (0,1)
The Coordinates of 2- (5,8)
The Coordinates of 3- (9,2)
The Coordinates of 4- (10,9)
The Coordinates of 5- (1,9)
The Coordinates of 6- (14,10)
The loads are 800, 300, 200, 200, 400, 100 respectively
A) The most optimal X coordinate of Warehouse = (0+5+9+10+1+14)/6 = 6.5
The most optimal Y coordinate of Warehouse = (1+8+2+9+9+10)/6 = 6.5
The coordinates of warehouse with equal load is (6.5,6.5)
This coordinates corresponds to the warehouse A.
B) The most optimal X coordinate of Warehouse = (800*0+300*5+200*9+200*10+400*1+100*14)/(6*2000) = 3.55
The most optimal Y coordinate of Warehouse = (800*1+300*8+200*2+200*9+400*9+100*10)/(6*2000) = 5
Thus the optimal position of warehouse with stated load is (3.55,5)
It can be visibly be seen that Warehouse B is the nearest point to this optimal position.
Note: If the problem is little complicated, you can use the distance formula and the one with lowest distance is the most optimal point
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