All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Peoples Day (Posted on 2019-08-12) Difficulty: 3 of 5
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).

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Using Calculus Comment 3 of 3 |
The function to be maximized is n*365*(364/365)^n.
It suffices to maximize n*(364/365)^n.

The first derivative is (364/365)^n + n*(364/365)^n*ln(364/365).

Setting this equal to 0 and solving gives
  n = -1/ln(364/365), which is approximately 364.5

So n = 364 or 365.

Based on earlier posts, they are both solutions.

  Posted by Steve Herman on 2019-08-14 08:44:55
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (2)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information