How is this solved?

Exercise 1 ( 30 points) Consider the following one-period model. Suppose that Cookie Monster's production function is given by Y = zx/KNd with z = 16 and K = %. Suppose also that w = 1. (a) Write his prot maximization problem, nd optimal labor demand N d\" and compute the maximized prot 7r. (b) Suppose that Cookie Monster's utility function is given by u(c, l) = c + 4vl + 2. Given to and 7r found in part (a), h = 16 and G = T = 2, write his utility maxi mization problem and nd his optimal consumption bundle c\" and 1*. (c) Write the production possibility frontier as a function of l. ((1) Would the labor market clear with the labor demand and supply found in parts (a) and (b)? Justify. If not, is u) too high or too low? In which direction does the labor market push to? (e) Compute the equilibrium (Hint: You may start from labor market clearing condition then nd numerical values for w, Nd, N\