Suppose a restaurant produces meals (M) using two production inputs: kitchen equipment (K) and cooking staff (L). The maximum number of meals the restaurant can produce with these inputs is the result of a technological process described by:M=K1/3L1/2. Suppose the wage ratew= 3and the rental rate for capital isr= 2.

1. (a)Find the long-run cost-minimizing input choice to produceM= 32.
2. (b)Now suppose that the firm is making a short-run decision but they currently haveK= 72Solve the short-run cost minimization problem to find the quantity of Labour demanded by the firmL.
3. (c)Calculate the Total CostTCresulting from the firm decisions you have found in parts 2a) and 2b). Using your calculations, explain whether the firm can do better in the long-run or the short-run.
4. (d)Re-solve the long-run problem in part 2a) keep M as an unknown variable. Find the firm's demand functions for labourL(M)and captialK(M)