At Perplexia Inc Headquarters, the puzzlewriting department has been hugely understaffed as of late. President and CEO, levik, wants the Recruiting Department to hire a number of puzzlewriters, and, to that end, has asked Division Director of Algorithms, Charlie, to come up with a way of determining how many recruiters are needed to focus on hiring new puzzlewriters to reach their hiring goal.
Any given recruiter can be working on filling p positions at once.
Any given position takes d days to be filled by a recruiter.
The hiring goal is to have h new puzzlewriters total, and the goal date to accomplish this is g days from today.
You may assume there are already enough recruiters available; they simply need to be told which position to focus on filling.
How many recruiters are needed to hire the required number of puzzlewriters by the deadline, in terms of p, d, h, and g?
let F(x) be the floor of x and C(x) be the ceiling of x
so we can break down time into intervals of length D days
in each of these intervals, each recruiter can recruit P puzzlewriters
in G days there are F(G/D) intervals
thus by the G day deadline, each recruiter can recruit F(G/D)*P
if there are R recruiters then we have
F(G/D)*P*R puzzle writers hired
thus we need F(G/D)*P*R>=H
or
R>=H/[F(G/D)*P*R]
since R needs to be an integer we have
R=C(H/[F(G/D)*P*R])

Posted by Daniel
on 20141010 12:59:49 