Suppose that the production function is q=F(L,K)=(KL) 1/3. The output and input prices are (p,w,r)=(1,1,1) ∗∗ Part a Derive the long-run cost function C(q) ∗∗ Part b Solve the long-run profit maximization problem directly: max K,L 1∗F(L,K)−1∗L−1∗K and find the profit-maximizing output. [Hint: there are two first-order conditions, and you need to solve them jointly.] ∗∗ Part c As an alternative to Part b, solve for the profit-maximizing output using the long-run cost function you derived in Part a.