EDIT: YOU CAN IGNORE THE THINGS BELOW. I FOUND OUT MY ERROR AND FINISHED THE PROBLEM. HERE IS THE NEW PROBLEM I AM HAVING:

I am doing a multivariate (3 variables) optimization problem, but the variables are discrete (number of advertisements in newspapern, magazinem, and televisiont). I got the 3 answers,

n= 28.78490

t = 4.9103

m = 8.4661

but I need them in integer form because thats in the context of the problem. I can make a large table of values to find out the maximum values, however is there a more mathematical way? and rounding doesnt do it, cause the maximized integer values are 30, 5, 8

I posted this in the calculus section, but it applies here as well i guess,

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!