On any workers birthday, all workers have a holiday. Other than these holidays, the workers work every day of the year (365 days total). The employer wants to maximize the expected total number of days worked per year. How many workers should be hired?
The simplest answer seems to be 182 or 183 (365/2). This does not take the probabilities of the different birthdays into account, though. How would I go about finding the EXPECTED total using probability distributions?
Thank you for your help.
2007-05-26 07:49:31 · 3 answers · asked by hobolord84 1 in Science & Mathematics ➔ Mathematics
Something is missing from the question, becaue hiring zero workers leaves the expected days at 365 (which is clearly maximal).
What detail you have left out is some parameter around his staffing requirements. Does he need, say, at least 20? Are you trying the maximize the number of (person)(days) = (# workers) x (#number of days out of 365)?
As worded, the answer is to hire zero workers, but I am certain there is a missing consideration, yes?
2007-05-26 08:44:39 · answer #1 · answered by chancebeaube 3 · 0⤊ 0⤋
As a joke , I want to say 1/365. But, it is wrong. Meaning just hire one worker.
I do not know.
2007-05-26 17:34:18 · answer #2 · answered by Kandice F 4 · 0⤊ 0⤋
Or...he could hire as many as he wanted...all with the same birthday....
sorry, I answered for the points
2007-05-26 14:59:48 · answer #3 · answered by jassie192000 2 · 0⤊ 0⤋