Optimizing a Linear Function with Constraint: A Tutorial on Lagrange Multipliers

[quantumfireball]

First let me clarify this is not a homework question.
This part has cropped up as part of a small project i am doing on Cosmic microwave background.

How would i go about minimizing the function

f(x$$_{1}$$,x$$_{2}$$...x$$_{n}$$)=$$\Sigma$$*x$$_{i}$$*a$$_{i}$$

subject to the constraint:
$$\Sigma$$ x$$_{i}$$*(2*i+1)=constanta$$_{i}$$ are constants

 

[mathman]

Use Lagrange multipliers. See Wikipedia (or other Google reference) for tutorial.