1.Pavlov Bell Company PBC makes bell systems that it sells to a variety of custo

Question

1.Pavlov Bell Company

PBC makes bell systems that it sells to a variety of customers who incorporate them into home automation systems.

The company is looking to locate a new distribution center to serve its four largest customers. The location of each customer can be plotted on a grid, with coordinates as shown below, along with their annual unit purchases from Pavlov.

Assuming that freight rates are uniform throughout this area, calculate the appropriate coordinates for PBC's new distribution center on the same grid.

Explanation / Answer

Let the appropriate coordinates for PBC’s new distribution center = P,Q

This problem will be solved using center of Gravity method.

As per this method ,

Sum of annual volumes of all customers x P = Sum for all customers ( X coordinate x Corresponding annual volume )

Sum of annual volumes of all customers x P = Sum for all customers ( Y coordinate x Corresponding annual volume )

Thus,

( 1850 + 1400 + 2300 + 850 ).P = 200 X 1850 + 300 X 1400 + 100 X 2300 + 450 X 850

Or, 6400.P = 370000 + 420000 + 230000 + 382500

Or, 6400.P = 1402500

Or, P = 1402500/ 6400 = 219.14

Similarly ,

( 1850 + 1400 + 2300 + 850 ).P = 600 X 1850 + 300 X 1400 + 100 X 2300 + 200X 850

Or, 6400.P = 1110000 + 420000 + 230000 + 170000

Or, 6400.P = 1930000

Or, P = 301.56

APPROPRIATE COORDINATES FOR THE NW DISTRIBUTION CENTER = ( 219.14, 301.56)

APPROPRIATE COORDINATES FOR THE NW DISTRIBUTION CENTER = ( 219.14, 301.56)

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