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.
The minimum will occur when all junctures are 120 degrees.
Add points F:(253,109), G:(332,771) and H:(186,880) and connect BH, CH, HG, DG, GF, AF, EF
This gives a total length of about 1704.59 for a cost of about $54546.88
Posted by Jer
on 2007-02-05 11:56:03