3. Suppose that QED |nc.'s production function is given by F {L, K} = til-Lme, where L denotes the quantity of labor and K denotes the quantitl,Ir of capital. In addition, PL is the price of labor per unit of labor lie, the wage rate}, PHB is the cost of health benefits per unit of labor, and PK is the price of capital. a} Suppose that initially the price of labor [wage rate] is $12 per unit of labor (PL 2 512), the cost of health benefits is $4 per unit of labor [PHB = $4}, and the firm's marginal revenue is $4 per unit (MR = 54). Given the initial quantity of capital, Kn = 400, derive the firm's marginal revenue product of labor function, MRPL, and its marginal factor cost of labor function, MFCL. b] Suppose that QED initiallv employs 225 units of labor along with the 400 units of capital, i.e. (Lgu) = [225, 400). Calculate the firm's initial output level, On. ls the firm maximizing its short run prots by hiring L0 = 225 units of labor? Explain. If not, calculate the short run profit maximizing quantity of labor, L5R*, and the 5R profit maximizing output level, (15