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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    Can someone please help me set up this problem?

    Find the larger of two numbers whose sum is 30 for which the sum of their squares is a minimum.
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  2. #2
    Senior Member DeMath's Avatar
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    Let the first number x_1 and the second number x_2.

    Then f\left( {x_1 ,x_2 } \right) = x_1^2  + x_2^2  \to \min and x_1+x_2=30\Rightarrow.

    \Rightarrow x_2=30-x_1\Rightarrow f\left( {x_1 } \right) = x_1^2  + \left( {30-x_1} \right)^2  \to \min

    Do you undestand?
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  3. #3
    Member Last_Singularity's Avatar
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    Quote Originally Posted by abclarinetuvwxyz View Post
    Can someone please help me set up this problem?

    Find the larger of two numbers whose sum is 30 for which the sum of their squares is a minimum.
    Denote these two numbers to be x and y.

    #1: Their sum must be 30, so: x+y=30, or y=30-x

    #2: And you want to minimize: x^2+y^2

    Given #1 as a constraint, #2 becomes: x^2+(30-x)^2. Differentiate this expression, set it equal to zero (to minimize), and find x
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