You are asked to determine a location for a recycling depot serving three urban

Question

You are asked to determine a location for a recycling depot serving three urban centres. They are: 1. Smallville, population 1,200, at grid location (8.8, 2.8); 2. Bigburg, population 1,400, at grid location (3.5, 8.1); and 3. Middleton, population 900, at grid location (7.8, 6.2).

It is determined that planners would prefer to have the depot in either Bigburg or Middleton (although it will serve all three centres). Using metropolitan distances, determine the load-distance scores for both Bigburg and Middleton and make a recommendation as to which town should have the depot.

Explanation / Answer

For depot at Bigburg

Distance from Bigburg to Smallville = |8.8 - 3.5| + |2.8 - 8.1| = 10.6
Load of Smallville = 1200
So, Load x Distance = 1200 x 10.6 = 12,720

Distance from Bigburg to Middletown = |7.8 - 3.5| + |6.2 - 8.1| = 6.2
Load of Middletown = 900
So, Load x Distance = 900 x 6.3 = 5,580

So, total load-distance = 12,720+5,580 = 18,300

For depot at Middletown

Distance from Middletown to Smallville = |8.8 - 7.8| + |2.8 - 6.2| = 4.4
Load of Smallville = 1200
So, Load x Distance = 1200 x 4.4 = 5,280

Distance from Middletown to Bigburg = |3.5 - 7.8| + |8.1 - 6.2| = 6.2
Load of Bigburg = 1400
So, Load x Distance = 1400 x 6.2 = 8,680

So, total load-distance = 5,280+8,680 = 13,960

So, Moddletown is the better option with respect to the load-distance score.

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