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Math Help - Optimization problems

  1. #1
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    Optimization problems

    I need some help doing some simple optimization problems. I really don't have any clue how to do them. The concept is completely lost on me.

    Let's start with this:
    Find a positive number such that the sum of and is as small as possible.

    Can someone give me a simple, step-by-step approach on how to solve these (emphasis on simple)?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by G-Rex View Post
    I need some help doing some simple optimization problems. I really don't have any clue how to do them. The concept is completely lost on me.

    Let's start with this:
    Find a positive number such that the sum of and is as small as possible.

    Can someone give me a simple, step-by-step approach on how to solve these (emphasis on simple)?
    First put:

    <br />
y=16 x + \frac{1}{x}<br />

    Then your question is asking you to find x>0 which makes y as small as possible. What this is asking is for you to find the minima for y for positive x.

    The usual way to do this is to find the solutions of:

    <br />
\frac{dy}{dx}=0<br />

    In your case there is only one solution for positive x, and that is the answer you seek.

    RonL
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