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Connecting the Points (Posted on 2007-02-04) Difficulty: 2 of 5
Five major buildings on a campus have coordinates A(0,0), B(0,800), C(200,1000), D(400,800), and E(400,0) (where the x and y axes are scaled in units of meters). Roads must be constructed to connect all of these buildings at a cost of $32 per linear meter (using a standard road width).

So, for example, if the point F has coordinates (200,400) and straight roads are built between A & F, B & F, D & F, E & F, and C & D, almost 2072 meters of road would be needed to connect the buildings at a cost of $66,294. to the nearest dollar.

Given a road construction budget of $55,900. for this project, show how you might connect the buildings within the budget constraints.

No Solution Yet Submitted by Dennis    
Rating: 4.0000 (1 votes)

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Solution A solution | Comment 1 of 8
Add a point F at (200,115), and connect A+F, E+F, C+F and B+D.

2*√(200+115) + 885 + 400 = 1746.4

1746.4 * 32 = $55,885

  Posted by TamTam on 2007-02-04 15:24:53
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