2. [25 Points] Consider the production function y = L, K) = 2L1/4K1/2 where L is labor and K is capital. Price per unit of the labor is w, price per unit of the capital is r, and the price per unit of the output is p. (a) [10 Points] In long-run, if the rm's objective is to maximize its prot, what are the factor demand functions of labor and capital? (b) [10 Points] What is the optimal output level :2} and the maximum prot. (c) [5 Points] If m = l, 1" = 2 and p = 5, does the rm will stay in business or stop the production