## Cobb-Douglas Production function help

Hi there,

I'm currently struggling with an economics problem and was hoping you guys could help me. I'm not trying to cheat on homework or anything, I have the answer and will supply it, I just need to know how to get there. I have an exam on this coming up and am completely useless at solving these problems. I hope you guys can help me. Anyway here's the problem:

QUESTION

A firm has the production function of the Cobb-Douglas.

Y=A.K^0.5 .L^0.5

L=50
A=300

The nominal interst rate (i) in the economy is 10% and the inflation rate \$%. Capital depreciates at a rate of 10% per year.

Find the optimal amount of capital this firm would be willing to employ.

....now have the answer from the answer page (this is an old mock exam) and I need to know the method used to get to the answer which is:

K*=4,430.5
Net I= K*-Ko=2,430.5
Gross I = Net I + depreciation = 546.434 + 0.1*2000 = 2,630.5

So how are the above answers calculated from the given information, as much help as you could give would be very very useful, sorry it's a long question. Many many thanks in advance.

Zeeky