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 units of capacity should the company sell with long-term contracts to maximize profit?