The production function for a firm is p(x, y) = 68x"y"", where x and y are the number of units of labor and capital utilized. Suppose that labor costs $102 per unit and capital costs $544 per unit and that the firm decides to produce 8704 units of goods. Determine the following. (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 102x + 544y, subject to the constraint 8704 - 68x*y" = 0. x= 256, y= 16 (Type exact answers in simplified form.) (b) Find the value of at the optimal level of production. A= 4 (Type an exact answer in simplified form.) (c) Find the expressions for marginal productivity of labor and marginal productivity of capital. Then find the ratio of marginal productivity of labor to marginal productivity of capital at the optimum level of production and the ratio of unit price of labor to unit price of capital and determine the relationship between the ratios. 11 marginal productivity of labor = 51x y* 3 3 marginal productivity of capital = 17x*y Determine the marginal productivity labor and marginal productivity capital at the optimum level of production and then compare the ratios. marginal productivity of labor marginal productivity of capital unit price of labor unit price of capital 16 (Simplify your answers.)