1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Optimization number question

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum.

    2. Relevant equations



    3. The attempt at a solution

    let a,b represent the two non negative numbers
    a=x
    b=30-x
    So, x^2+(30-x)^2=s, where s is the sum of their squares
    After expanding, the derivative is:
    s'=4x-60
    let s'=0, then x=15.
    The interval for possible x values is 0≤x≤30.
    So let us check which value gives a maximum.

    s(15)=450
    s(0)=900
    s(30)=900

    Therefore, the two non-negative numbers are 0 and 30. Is this right? I ask because the solution on a worksheet I have indicates that the two numbers are 15 and 15.
     
  2. jcsd
  3. Apr 23, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are correct that the maximums occur at the ends. Probably a typo in the problem. Maybe they meant minimum.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Optimization number question
  1. Optimization question (Replies: 1)

  2. Optimization Question (Replies: 3)

  3. Optimization Question (Replies: 1)

Loading...