A transportation company must decide how to sell its capacity. They have several options as contracts. If they sell some portion of their capacity with long-term contracts they will earn $1500/m2. However, if they don't sign long-term contracts but sell their capacity at the spot market, the expected future price will be $2000/m2. Consider a specific day, where the companys capacity is 70 units. The company expects that the spot market demand is normally distributed with a mean of 65 and a standard deviation of 10. On average, it costs the company $1000 in fuel, handling, and maintenance to fly a cargo unit.

a) Suppose the company relied exclusively on the spot market, i.e. no long-term contracts were signed. What would be the expected profit of the company?

b) Suppose the company relied exclusively on long-term contracts. What is the expected profit?

c) If the company uses a booking limit of 10 kg for the long-term contracts, what is the probability of meeting the spot market demand?