Zamatia makes sunglasses at a cost of $35 and sells them to Umbra Visage for $75. Umbra Visage sells them for $115 and salvages left over inventory for $25 per unit. Suppose demand for this type of sunglasses follows a normal distribution with mean 250 and standard deviation 125. a) Consider the decentralized supply chain scenario. How many sunglasses should Umbra Visage order to maximize its expected profit? b) Given the order quantity in part a), what is Umbra Visage's expected profit? c) Given the order quantity in part a), what is Zamatia's expected profit? What is the total supply chain profit? d) What would be the expected profit of the supply chain if it was centralized (vertically integrated)? Suppose Zamatia is thinking of offering a buy-back contract to Umbra Visage. e) If the buy-back price is 65, how many sun glasses should Umbra Visage order to maximize its expected profit? f) What is the buy-back price that coordinates the supply chain?