Consider the following production function yf$($z$)$ z$/2/2$ Assuming that the price of output is p and the prices of inputs are w$1$ and w$2$ respectively, a$)$ State the firm's profit maximization problem $(1$ mark$)$ b$)$ Derive the firm's factor demand functions for z$1$ and z$2(6$ marks$)$ c$)$ Derive the firm's supply function. $(2$ marks$)$ d$)$ Derive the firm's profit function. $(2$ marks$)$ e$)$ Verify Hotelling's Lemma for q$($w$.$p$),$ z$1($w$.$p$)$ and z$($w$,$p$)$