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.

(In reply to Picture of Optimized solution by Jer)

1) The link seems to be broken.

2) F is where the ray from G passes through arc AF.  I don't see mention of a ray going down and to the left from F before the "until...".  F and A are merely connected by a line segment.  When reconstructing what you say in the earlier part of the construction, I see the need for two adjustments: one for H and one for G, not just for H.  I do get about the same answer as yours, but I did leave the default precision to two decimal places.

Edited on February 5, 2007, 5:25 pm

Posted by Charlie on 2007-02-05 17:24:20