(a) Suppose we have the following production function: Q = K/3L2/3 Suppose K is fixed in the short- run at 27. State the firm's short-run cost minimization problem given the fixed input. Discuss. (b) Let r $20 and w = $30. Derive the short-run cost function so that we have costs as a function of Q: eg C(Q) = ? Show your work/reasoning. (c) State the firm's profit maximizing problem. (d) Let P $60. Find optimal output when r = $20 and w = $30. You can do this in a table or mathematically. What are profits? (e) A break-even price is one where the best a firm can do is earn zero profits in the short-run. That is, total revenues equal total costs. What is the break-even price if r = $20 and w = $30? Explain/show. (f) The shut-down price is one where the firm will set Q = 0 in the short-run. That is, any positive output worsens losses given the fixed costs. What is the shut-down price if r = $20 and w = $30? Explain/show.