Calculus II: Optimisation question below! :)

Question

mortonsalt · Answer

The cost of production of books is equal to
$$P=5X^{\frac{2}{3}}Y^{\frac{1}{3}}$$
Wherein X is the amount of labour and Y is the amount of capital investment.

If it costs $20 per unit labour and $30 per unit of capital investment, how much of a $20000 budget should be spent on labour in order to maximise the production of books?

phi · Answer

Lagrange multipliers ?

ganeshie8 · Answer

maximize $5x^{2/3}y^{1/3}$
subject to $20x+30y = 20000$

ganeshie8 · Answer

You just have to run it through the method of lagrange multipliers. 
Do you have any difficulty in understanding the method in general ?

mortonsalt · Answer

@ganeshie8, I was just unsure of how to start. :) Thank you!

ganeshie8 · Answer

Ahh okay, just so you feel confident, you may use wolfram to double check your final answer. http://www.wolframalpha.com/input/?i=maximize+5x%5E(2%2F3)y%5E(1%2F3),+20x%2B30y+%3D+20000

ganeshie8 · Answer

Careful though, the final answer is not 2000/3.