Given some function, and given constant $K$:
$$f(x,y,z) = x*y*z$$ $$a*x+b*y+c*z=K$$
How would $a$, $b$, and $c$ be determined such that function $f$ is maximized?
My first intuition tells me to take the derivative of $f$ and determine where that is zero in order to find a maxima / minima. Frankly speaking, I am not well versed in Calculus so I would think that taking the partial derivative with respect to $f$ would cause the left hand side to be zero. That does not seem correct.
As a bonus, the real equation I am attempting to solve is this. Given $K$ and $batk$:
$$damage(katk,fatk,pcrt,kcrt,kdmg)=(1+katk+fatk/batk)*(1+pcrt*kcrt)*(1+kdmg)$$ $$a*katk/0.05+b*fatk/18+c*pcrt/0.033+d*kcrt/0.066+e*kdmg/0.05=K$$
I believe I could solve this equation once I understand the simpler case