help with layman terms algorithm development?

*To*: mathgroup at smc.vnet.net*Subject*: [mg126592] help with layman terms algorithm development?*From*: luke wallace <lukewallace1990 at gmail.com>*Date*: Mon, 21 May 2012 06:00:01 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

ok, i have a fairly simple problem, that will probably look really complicated in a computer solving algorithm. i'm not trying to implement it into mathematica yet i just want to get an idea of what it would look like in general terms here's the problem: you have a room that is 130 feet wide and 65 feet long you need to cover the entire floor area with a life safety system - fire sprinklers. each sprinkler covers a floor area of 15 ft x 15 ft, or 225 sq ft. sprinklers cannot be placed anywhere on the ceiling - there are beams you have to space away from, but still cover the floor area underneath the beams. because of this, spacing won't be so mathematically simple. you need to be spaced away from beams at least 3 ft according to a rule book. the sprinklers can only throw water 7.5 out in all directions, so if you have to be at least 3 ft away from the centerline of the beam, your option s for sprinkler spacing from the beam are >3ft but <7.5 what is the optimal spacing algorithm in general terms, for all possible orientations of beams?