Chris runs a firm that hires quantities x1 and x2 of inputs 1 and 2 at prices w1 and w2. The production function is given by f (x1, x2) = 1 3 ln x1 + 1 3 ln x2 2.1 [12 points] Suppose the market in which this firm produces is perfectly competitive, with output price p. Find the optimal quantity of output for the firm and the firm's profit. Do not worry about simplifying your expressions once you have them. (You want to maximize profits using the input-oriented approach.) 2.2 [6 points] Now suppose that p = 3, w1 = w2 = 1/3. Assume that in order to operate in this market, the firm must make a rental payment of R = 2 to the owner of the location at which the firm does business. This payment is the same no matter how much the firm produces. Find the firm's optimal quantity of output and the firm's profit.1