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 = K ^1/3 L ^1/2 . Suppose the wage rate w = 3 and the rental rate for capital is r = 2.

(a) Find the long-run cost-minimizing input choice to produce M = 32.

(b) Now suppose that the firm is making a short-run decision but they currently have K = 70 Solve the short-run cost minimization problem to find the quantity of Labour demanded by the firm L .

(c) Calculate the Total Cost T C. Using the calculations, explain whether the firm can do better in the long-run or the short-run.