# Lagrange Multiplier Optimization

Please explain the two constrained optimization problems using a lagrangian multiplier.

Problem one as follows:

Maxamize f(x,y)= x ^1/3 y^2/3 subject to x+2y=100

The next one is a three variable problem max f(x,y,z)=x ^ 1/4 y ^ 2/4 z ^ 1/4 subject to 2x+2y+2z = 100

I understand how to set the problem up with partial derivatives, but I am having trouble simplifying the derivatives with positive exponents and working out any further. Any assistance is much appreciated.

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#### Solution Summary

This solution is comprised of a detailed explanation to help with two constrained optimization problems using a lagrangian multiplier.

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