# Homework Help: Need help to maxmize function

1. Sep 1, 2010

### Gekkoo

1. The problem statement, all variables and given/known data

I need help to maximize the below function:

2. Relevant equations

Maximize u(x, y) = x^α * y^β subject to Ax + By = m

Any help is greatly appreciated!

/ Gekkoo

Last edited: Sep 1, 2010
2. Sep 1, 2010

3. Sep 1, 2010

### HallsofIvy

I'm a big fan of "Lagrange Multipliers" but if you don't know that method, you could just write y= (m- Ax)/B so that $x^\alpha*y^\beta= x^\alpha*(m-Ax)^\beta/B^\beta$. Now, do you know how to find maxima and minima for that?

4. Sep 2, 2010

### Gekkoo

1 Solve constraint for y:

y=(m-Ax)/B

2 Plug into objective function:

u=x^α*[(m-Ax)/B]^β

3 Diff w.r.t. x & equate to zero to get critical point:

FOC: x^α*ln(x)*????=0

4 Solve FOC for x:

x=????

5 Plug that into constraint to get value for y:

y = (m-A[????])/B

6 Than I have a candidate solution & need to check SOC of objective function w.r.t x!