Question 4 (25 points) Mizuno Corporation produces and sells running shoes. The marketing division {the downstream division] of Mizuno faces the following direct market demand function as follows: Q = 120 - 0.5P. where Q Is the number of pairs of shoes and P is the price of a pair of shoes. The total cost of assembllng and selling shoes {excluding the leather} is TCu = ZOQ + 60. Production of each pair of shoes requires 1 square yard of leather. The leather is shaped and cut by the Form division of Mizuno {the upstream division}. The Form division's only customer is the marketing division. That means there is no external market. The total cost function for leather is TCU=U.EQ.+20QU+4U. where Q; is the quantity of leather produced. (Hint: use Transfer pricing model to answer this question] 4.1 {7 points) Write down the prot functions. See slide#34, Ch 9 and follow Equations {a}. (b). and {c}. - Profit function of Downstream division {up}: Tlo = - Profit function of Upstream division {no}: No = a Total prot function in}: 11: 4.2 (7 points) Determine the profit-maximizing quantity of shoes (Q*), the quantity of leather (Q ) and the price of a pair of shoes (P*). Q* = units. units. P* = $ 4.3 (4 points) Determine the optimal transfer price (Py). . P. = $4.4 I? polnts] Use the prot functions of your answer in {4.1). determine the prots earned by the downstream division {no}, the upstream division {u}. and total prots {rt}