Find the maximum of subject to the constraint .
Using Lagrange multipliers, make a new function:
Take the partials of with respect to , , and and set them equal to zero.
This is a trick. Notice that if you multiply the last three equations by , , and respectively and then add them, you can factor out a term that is equal to . So multiplying,
Now add these equations to get
Plug this value of lambda back into 1), 2), and 3) to get: