An air cargo company must decide how to sell 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 and there is ample demand. If long-term contracts are not signed for all its cargo space capacity, then the company can sells its remaining cargo space on the spot market. The spot market price is volatile but the expected future spot market price is around $2,100 per standard unit of space. In addition, the 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 a mean of 65 and a standard deviation of 20. On average, it costs the company $330 in fuel, handling, and maintenance to fly a unit of cargo.
A. Suppose the company is willing to use both the long-term and spot markets. How many units of capacity should the company sell with long-term contracts to maximize expected profit? [Show your data values and approach.]
B. Does your answer to the question above increase or decrease if the spot market demand was Poisson distributed with mean 65? Why does it increase or decrease?