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.

Add a point F at (200,115), and connect A+F, E+F, C+F and B+D.

2*√(200²+115²) + 885 + 400 = 1746.4

1746.4 * 32 = $55,885

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