[SOLVED] Partial Differentiation and Lagrangian method: help me

EDIT: I SOLVED IT, NEVERMIND!!

Ok, So attached I have a doc file with a couple pages of math work in it...it has text and math and is pretty self-explanatory. However, towards the end, I am wrong and I don't know why.

here is the problem i was doing: located in the first attached, titled:" Assignment 1 Productivity Method of Valuation"

my work is the next attachment, titled "econ"

using excel, i found the values of N, M, and T that maximize P. they are ~28.78, 8.47, 4.91 (for the problem, which has to be integers though, it is 30, 8, 5)
now i am trying to maximize the profit using regular math by hand. I'm using the Lagrange method and it seems to be working out..for some reason when i plug in the excel-found values into any of the equations i got (eq. 6.2 and beyond), it doesnt work. so maybe you guys can help me.

thanks a lot!