At Perplexia Inc Headquarters, the puzzle-writing department has been hugely understaffed as of late. President and CEO, levik, wants the Recruiting Department to hire a number of puzzle-writers, 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 puzzle-writers 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 puzzle-writers 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 puzzle-writers 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 puzzle-writers
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])
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Posted by Daniel
on 2014-10-10 12:59:49 |
solution
