Problem 8-15 An analysis of sltes for a distribution center has led to two possi

Question

Problem 8-15 An analysis of sltes for a distribution center has led to two possible sltes (L1 and L2 on the map). The sites are comparable on every key factor. The one remalning factor is the center of gravity. Use the center of gravity method to select the better site. Monthly shipments will be the quantities listed In the table. Referencing the graph below, all destination locations occur at whole number x and y coordinates. (Round your answers to 2 declmal places.) D2 D5 L2 L1 D1 D4 D3 Destination Quantity D1 D2 D3 D4 145 800 758 35e 875 Use the center of gravity method to select the better site. Center of Gravity: Better site ickto select)

Explanation / Answer

Let the coordinate of the required site be ( P. Q)

Therefore , using center of gravity method :

Sum of quantities to various locations x P = Sum ( Quantity x Corresponding X coordinate) for all 5 locations

Or, ( 145 + 800 +750 + 350 + 875 ) x P = 1 x 145 + 2 x 800 + 3 x 750 + 4 x 350 + 5 x 875

2920.P = 145 + 1600 + 2250 + 1400 + 4375

2920.P = 9770

P = 9770 / 2920

Or, P = 3.345 ( 3.35 rounded to 2 decimal places )

Sum of quantities to various locations x P = Sum ( Quantity x Corresponding X coordinate) for all 5 locations

Or, ( 145 + 800 +750 + 350 + 875 ) x Q = 2 x 145 + 4 x 800 + 1 x 750 + 2x 350 + 3 x 875

Or, 2920.Q = 290 + 3200 + 750 + 700 + 2625

Or, 2920.Q = 7565

Or, Q = 2.59

Therefore Coordinates of the required site is ( 3.35, 2.59 )

CENTER OF GRAVITY

X = 3.35

Y = 2.59

Following are evident from the given graph:

Coordinates of L1 = ( 2.5 , 2.5)

Coordinates of L2 = ( 3.5, 2.7 ) approx.

Center of gravity ( 3.35, 2.59 ) is thus closer to L2 . Therefore , better site is L2

BETTER SITE L2

CENTER OF GRAVITY

X = 3.35

Y = 2.59

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