I am attempting to model the following equation with 3 variables (H, M, and S) and 1 constant (C):
D = .05*H*M + .05*S*(M+C)
or, when factored
D = .05*M (H+S) + .05*C(S)
It'd be a simple matter to calculate the value of D at any point in the formula (just plug in the variables), but I'm more interested in the relationship between S, M, and H; I'd like to be able to determine how much D will change (dD) when I increase S, M, or H (or some combination thereof).
It's been a while since I've used partial derivatives, but I believe that's what I'd need to use to answer this?
I think I've got a handle for single values (i.e., partial derivative with respect to M only), but how do I calculate the expected change of both (for instance) increasing H by 1 and decreasing S by 1?