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 Connecting the Points (Posted on 2007-02-04)
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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 re: A solution | Comment 2 of 8 |
(In reply to A solution by TamTam)

The 115 is a good approximation to 200/sqrt(3), making angle AFE close to 120 degrees, an optimizing angle for this sort of thing, where three lines meet.
 Posted by Charlie on 2007-02-04 15:40:49

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