Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm operates with the production function $Q = L^aK^bR^c$. The firm chooses labor and capital to maximize profit.
a. Derive the firm’s profit function. $\pi$
b. Derive the first-order conditions FOC for profit maximization.
My Question is regarding FOC, since the firm chooses labor and capital to maximize profit, do I look at this as a problem with simply two endogenous variables mainly labor $(L)$, capital $(K)$, hence the FOC are the partial derivative of the proofit function $w.r.t. L$ and $K$. ($\pi_L$ and $\pi_K$) or should I include $\pi_R$ in my solution