Question 2. (9 points) A group of people wished to charter a boat for a voyage around the world (their plans have since changed...). The charter company with which they were negotiating charged a fee of $1000 per person for groups of 100 people or less, and decreased the fee by S5 per person more than 100 (so, for example, a group of 104 would pay $980 per person). The charter company has fiat expenses of $40,000 plus an additional $200 per passenger. In this problem you will determine how many passengers would have marimized the charter company's profits had everything not gone haywire. (a) (1 points) Recall that Profit = Revenue - Cost. Using this fact, find a formula P(n) for the profit which is valid when there are n = 100 passengers or fewer. Is the revenue ever decreasing in this range? (b) (2 points) Now find a formula for the profit which is valid when there are more than 100 passengers. (c) (3 points) In which part of the domain (n 100) will the maximum be located? Find P'(n) for the formula that applies here. (d) (3 points) Finish the problem. Justify your answer! Page 2