Thread: 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)?

Originally Posted by G-Rex

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:



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

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



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

RonL