A company has the policy that any employee's birthday is a holiday for the entire company. How many people should the company employ if the expected value of the total number of "people-days" (the product of the number of employees and the number of days worked) is to be maximized?
Answer the question assuming that there are 365 days in a year, that each day is equally likely to be a birthday, and that the employees have no days off except for the birthday/holidays (i.e. no weekends off).
By starting with shorter 'years' I was able to derive a formula for n=days in a 'year' and m=employees
"people-days"=m*(n-1)^m/n^(m-1)
For n=365, google sheets couldn't extend a table that far so i went with WolframAlpha and found when m=364 or m=365 the function is maximized at 48943.5 "people-days"
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Posted by Jer
on 2019-08-12 13:36:04 |
Solution
