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QUESTION 3 (20 points) Party Hat Inc. is a manufacturer of party hats, primarily for the Halloween season. One of their popular products is the Elvis wig. The Elvis wig is produced in China, so Party Hat must make a single order well in advance of the upcoming season. The marketing manager of Party Hat expects demand to be 25,000 and the following is his entire demand forecast: Q Prob(D=Q) F(Q) 5,000 0.0183 0.0183 10,000 0.0733 0.0916 15,000 0.1465 0.2381 20,000 0.1954 0.4335 25,000 0.1954 0.6289 30,000 0.1563 0.7852 35,000 0.1042 0.8894 40,000 0.0595 0.9489 45,000 0.0298 0.9787 50,000 0.0132 0.9919 55,000 0.0053 0.9972 60,000 0.0019 0.9991 65,000 0.0006 0.9997 70,000 0.0002 0.9999 75,000 0.0001 1 The Elvis wig's price is E10. Its production cost is E7. Leftover inventory can be sold to discounters for E4.5. a. Suppose Party Hat orders 30,000 Elvis wigs. What is the chance they have to liquidate 5,000 or more wigs with a discounter? b. What is the optimal order quantity that maximizes expected profit? c. If Party Hat wants to have at least 99% service level, then how many Elvis wigs should be ordered? d. If Party Hat insists on a 100% service level for its customers, what is its expected profit