Help with Lagrangian expression!

If someone could try to explain the lagrangian expression to me, I'd greatly appreciate it. The textbook i have is not very good at explaining things and there doesn't even seem to be an example...

thanks in advance!

also, this is the question i need to apply it to:

A person's satisfaction (or utility) from playing tennis and golf is given by:

U = ln(G) + 4 ln(T)

where G is the number of hours spent playing golf and T is the number of

hours spent playing tennis. This person has 10 hours per week to devote to

these sports. However, each hour of playing tennis typically entails one hour

of waiting for an empty court, thus using up twice the time of actual play.

As a consequence, for example, if he spent 2 hours playing golf and 4 hours

playing tennis, he would have used up the full 10 hours of his available time.

a) What equation describes this person's time constraint?

So: 2T + G <or=10

b) What is the Lagrangian expression of this constrained maximization prob-

lem?

c) Use this Lagrangian expression to nd out the satisfaction (or utility)

maximizing choice of time to play golf and tennis.