E. A producer has two production processes, both using a single input, r, and both producing the same output, y. The first one produces output according to fi(11) = 120x7, the second one produces output according to f2(22) = 1022. The producer is in a competitive industry, and takes as given p, the price of y, and w, the price of r. E.1. Give the firm's cost function. E.2. Give the range of p's and w's for which the firm's supply function can be found, and explain why it cannot be found outside of that range. E.3. Give the firm's supply function, its input demand function, and its profit function over the range where these are defined. E.4. Using the envelope theorem, give the derivative of the firm's profit function with respect to p and with respect to w