Math Challenge (was: Help solving equation) Message #26 Posted by Geir Isene on 29 Dec 2010, 2:44 p.m., in response to message #1 by Geir Isene
To elaborate on the task at hand;
I am looking to see if a business area would benefit from a formalized process.
A task has the total cost (C) after N repetitions of c*N (where "c" is the cost of doing the task once). If N = n*y (where "n" is the number of times a task is done per year, and "y" is the number of years), we get the total cost of a task done over a certain number of years (or fraction(s) of years):
C = nyc (pun not intended) [#1]
If introducing a standardized process for the task gives an efficiency ratio of "E" (a number hopefully between 0 and 1), after the process is introduced we get:
C = nycE [#2]
But establishing a process has an initial cost of "I". To recuperate the cost, we get:
nyc - nycE > IR^y [#3]
where "R" is the needed return on investment: R = (1 + r/100) where "r" is the percentage needed as annual return on the investment. In some instances the initial cost is recuperated after a certain time, in other cases, the initial cost is never recuperated and a formalized process is not warranted.
If the task is repeated often and the cost of introducing a process is not too costly, it would be a sound business decision to formalize a process for the task - as is the case with an assembly belt production line. Other more unpredictable and emergent tasks are very seldom repeated and the initial cost is never recuperated.
The challenge is to solve equation #3 for y. Actually it would be good to create a program that would solve for any variable given the other variables in the equation (as in the Ohms Law program discussion recently).
I could settle for approximations instead of wild and complex equations as the real world cases are approximations in any case.
Take this as a math challenge :)
Any suggestions?
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