Question

(A) Use the appropriate location procedure to determine the optimal coordinates of a new machine based on the following assumptions. (Please show the details of your work: Not just the final answer). Traffic pattern. Rectilinear • Objective: Minimizing cost • Coordinates of the existing machines (5,2).(4.8) (10.12).(3,20),(7.7) • Total weight of material to be moved between the new machine and the existing ones: 11000, 27500, 22000, 3000 and 17000 pounds per week, respectively. (B) Calculate cost in distance-weight units

Answer 1

To minimize the cost, we will use the gravitational method to find the location

X-coordinate = sum total of (x-coordinate of current location * load) for all locations/sum total of loads

Y-coordinate = = sum total of (y-coordinate of current location * load) for all locations/sum total of loads

x-coordinate = (5*11000 + 4*27500 + 10*22000 + 3*3000 + 7*17000)/(11000 + 27500 + 22000 + 3000 + 17000) = 513000/80500 = 6.37 = 6

y-coordinate = (2*11000 + 8*27500 + 12*22000 + 20*3000 + 7*17000)/( 11000 + 27500 + 22000 + 3000 + 17000) = 685000/80500 = 8.51 = 9

Hence, the location coordinate is (6, 9)

Finding the distance-load:

Rectilinear distance = |X – Xc| + |Y – Yc|

x-coordinate	y-coordinate	distance	load	load-distance
5	2	8	11000	88000
4	8	3	27500	82500
10	12	7	22000	154000
3	20	14	3000	42000
7	7	3	17000	51000

Total load-distance = (88000 + 82500 + 154000 + 42000 + 51000) = 417500

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