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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Picture of Optimized solution | Comment 7 of 8 |
(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

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