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20 March, 05:20

The Burger Doodle restaurant chain purchases ingredients from four different food suppliers. The company wants to construct a new central distribution center to process and package the ingredients it uses in its menu items before shipping them to their various restaurants. The suppliers transport the food items in 40-foot tractor-trailer trucks. The coordinates of the four suppliers and the annual number of truckloads that will be transported to the distribution center are as follows:

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  1. 20 March, 05:41
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    Given Information:

    Site 1: x1 = 360, y1 = 180

    Site 2: x2 = 420, y2 = 450

    Site 3: x3 = 250, y3 = 400

    Solution:

    Xa = 200, Ya = 200, Wa = 75

    Xb = 100, Yb = 500, Wb = 105

    Xc = 250, Yc = 600, Wc = 135

    Xd = 500, Yd = 300, Wd = 60

    If centre of gravity is (x, y)

    then x = (200*75+100*105+250*135+500*60) / (75+105+135+60)

    x = 238

    then y = (200*75+500*105+600*135+300*60) / (75+105+135+60)

    y = 444

    Using centre-of-gravity method, location of distribution centre = (238,444)

    Using rectilinear distance,

    Load distance score of Site 1: 75 * (abs (360-200) + abs (180-200)) + 105 * (abs (360-100) + abs (180-500)) + 135 * (abs (360-250) + abs (180-600)) + 60 * (abs (360-500) + abs (180-300)) = 161550

    Load distance score of Site 2: 75 * (abs (420-200) + abs (450-200)) + 105 * (abs (420-100) + abs (450-500)) + 135 * (abs (420-250) + abs (450-600)) + 60 * (abs (420-500) + abs (450-300)) = 131100

    Load distance score of Site 3: 75 * (abs (250-200) + abs (400-200)) + 105 * (abs (250-100) + abs (400-500)) + 135 * (abs (250-250) + abs (400-600)) + 60 * (abs (250-500) + abs (400-300)) = 93000

    Site 3 tends to be optimal as it offers a lower distance ranking.
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