Problem 1: Campus bookstore sells premium chocolate gift boxes specially packaged for Valentine's Day every year. The order needs to be placed with a premium chocolatier two months in advance. Suppose that campus bookstore pays $25 for each box of chocolate that they order, and campus bookstore sells the chocolate gift boxes at $40 each. After Valentine's Day, campus bookstore can sell all unsold boxes of chocolate at 50% off. In case of a stock-out, 50% of the customers buy a teddy bear instead, and the rest of the customers walk away. The campus bookstore pays $20 for each teddy bear, and sells for $25 each. Since the teddy bears are non-perishable, the campus bookstore holds a very large inventory of teddy bears to satisfy all demand before or on Valentine's day. Assume that the total demand for the chocolate gift boxes before or on Valentine's day is Normally distributed with mean 200 and standard deviation 50. a) With the goal of profit maximization, how many boxes should be ordered by the campus bookstore two months before Valentine's Day? b) In this case, what is the expected profit of the chocolate boxes? c) In this case, what is the expected profit of the teddy bears that are from the stockout of the chocolate boxes? d) This year, the supplier of the chocolate boxes offers an additional delivery option of chocolate boxes at 12pm on Valentine's Day for an additional per-unit premium p. By then, the Bookstore will know for certain what the demand will be. Assume that inventory from the additional delivery can satisfy demand at any point in time. What is the maximum premium p the Bookstore would be willing to pay to exercise this option?