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If a producer's production function Is: f (zl,z2) = In Zl + In The price is wt for input zt, i = 1,2. The price of the output is r. (1) Find the supply function y(p) and profit function TT(p), where p Show that VTT(p) = y(p)_ (2) Given a production level q, please find the conditional factor demand z(w, q) and the cost function c(w, q) _ Show that Vc(w, q) = z(w, q). (3) Using the cost function in (2), rewrite the profit maximization problem and show that the maximal profit is the same with that in (l).