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February 24th, 2012, 09:27 AM  #1 
Newbie Joined: Feb 2012 Posts: 1 Thanks: 0  Scaling payouts over time
This isn't for homework or school so help anyone else who may need it first. I'm an English major (don't kick me out!) so I need some help. This didn't strike me as a collegelevel problem so I posted it here. Problem: There are multiple properties you can build. You can build an infinite amount of each one, constrained only by how much money you have. Each building pays out X amount (varying) every Y unit (varying) of time. Nominal amounts of money to be invested can be earned other ways (unrelated). Base cost of each building increases with each building of the same type. Goal: Make as much profit as possible in an unlimited time frame. Data Format: ==Format is as follows: base cost  amount of base cost increase per additional  payout/payout time== example: Z) 5000  500  250/3 hours Building Z costs $5000 to build the first one, the cost increases by $500 each ($5000 first, $5500 second, $6000 third, etc.), it pays $250 every three hours. The third building Z would cost $6000 and pay out $750 every 3 hours. Note that the buildings stack, so rather than three building Zs each paying out every 3 hours, owning three gives you one building Z that pays out $750 every 3 hours. Data: A) 1000  100  195/15 minutes B) 5000  500  260/20 minutes C) 60,000  6000  2600/2 hours D) 85,000  8500  3250/2 hours E) 400,000  40,000  7150/3 hours F) 2,000,000  200,000  65,000/5 hours G) 3,000,000  300,000  13,000/1 hour (seems out of place, but not a typo) H) 5,000,000  500,000  325,000/12 hours I) 20,000,000  2,000,000  650,000/8 hours J) 30,000,000  3,000,000  780,000/9 hours K) 40,000,000  4,000,000  1,040,000/10 hours L) 100,000,000  10,000,000  1,300,000/16 hours Question: How many of each build should be owned before justifying the purchase of a different type? At what quantity is a building no longer efficient to build? Are there buildings that should never be purchased? ex: 50 of A, then 50 of B, skip C, 35 of D (after 50 B), build 50 more of A, etc. I know this is a ridiculously long problem (at least in my eyes) with a lot of stuff to grasp. I've run into problems like this before but don't know how to solve them. If asked on many other forums before this one but no one is willing to help out, so hopefully one of you on a caffeine high with some time to spend can shed some light for me. E 
February 24th, 2012, 12:17 PM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,593 Thanks: 953  Re: Scaling payouts over time Quote:
Instead of 2 add'l buildings, let's make it 10 add'l: last one = 10,000; total invested = 82,500; 11 @ 250 = 2750 ; 82500/2750 = .03333... or 3 1/3 % So if "benchmark" is say 3%, then it's about time to get out of the "Z business"! Is that what you mean? How "realistic" is the list you're showing? Like: A) 1000  100  195/15 minutes. You spend $1000 and get it back within about 75 minutes? Ridiculous. Why does your data list show revenues differently; why ain't them all (as example) "per day"?  

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