Problem 1:Cachon and Terwiesch 16.9 (MBA Admissions). Each year the admissions committee at a top business school receives a large number of applications for admission to the MBA program and they have to decide on the number of offers to make. Since some of the admitted students may decide to pursue other opportunities, the committee typically admits more students than the ideal class size of 720 students. You were asked to help the admissions committee estimate the appropriate number of people who should be offered admission. It is estimated that in the coming year the number of people who will not accept the admission offer is normally distributed with mean 50 and standard deviation 21. Suppose for now that the school does not maintain a waiting list, that is, all students are accepted or rejected.

a. Suppose 750 students are admitted. What is the probability that the class size will be at least 720 students?

b. It is hard to associate a monetary value with admitting too many students or admitting too few. However, there is a mutual agreement that it is about two times more expensive to have a student in excess of the ideal 720 than to have fewer students in the class. What is the appropriate number of students to admit? (Hint: think how to express the critical ratio)

c. A waiting list mitigates the problem of having too few students since at the very last moment there is an opportunity to admit some students from the waiting list. Hence, the admissions committee revises its estimate: It claims that it is five times more expensive to have a student in excess of 720 than to have fewer students accept among the initial group of admitted students. What is your revised suggestion?

Problem 2:Cachon and Terwiesch 16.10 (Air Cargo). An air cargo company must decide how to sell its capacity. It could sell a portion of its capacity with long-term contracts. A long-term contract specifies that the buyer (the air cargo company's customer) will purchase a certain amount of cargo space at a certain price. The long-term contract rate is currently $1,875 per standard unit of space. If long-term contracts are not signed, then the company can sell its space on the spot market. The spot market price is volatile, but the expected future spot price is around $2,100. In addition, spot market demand is volatile: sometimes the company can find customers; other times it cannot on a short-term basis. Let's consider a specific flight on a specific date. The company's capacity is 58 units. Furthermore, the company expects that spot market demand is normally distributed with mean 65 and standard deviation 45. On average, it costs the company $330 in fuel, handling, and maintenance to fly a unit of cargo.

a. Suppose the company relied exclusively on the spot market, that is, it signed no long-term contracts. What would be the company's expected profit?

b. Suppose the company relied exclusively on long-term contracts. What would be the company's expected profit?

c. Suppose the company is willing to use both the long-term and the spot markets. How many units of capacity should the company sell with long-term contracts to maximize revenue?

d. Suppose the company is willing to use both the long-term and the spot markets. How many