A cruise line offers a cruise ship weekend trip for the baseline fare of $1000 per passenger. The ship can accommodate up to 250 passengers.

No credit for work submitted without the introduction of your notation (what letters you choose for what quantities) and without any picture or table.

If more than 100 passengers sign up for the same weekend trip, the price per person for all passengers is reduced by $5 for each additional passenger beyond the number of 100 passengers: for example, if 101 people sign up for a weekend trip, the price per person is 995 dollars (the $1000 baseline minus $5 discount), if 102 people sign up for a weekend trip, the price per person is 990 dollars (the $1000 baseline minus $5x2=$10 discount), and so forth.

a) What number of passengers and what price per person (on a weekend trip) maximizes the total revenue of all fares sold for the weekend trip?

b) What is the maximum revenue per weekend trip? The fixed cost (fuel and maintenance) to the cruise line for operating the cruise ship is $40000 per weekend trip. The variable cost (food, cleaning, entertainment) per passenger (per weekend) is $200.

c) What number of passengers and what price per person (on a weekend trip) maximizes the total profit (all fares sold minus the total cost) for the weekend trip?

d) What is the maximum profit per weekend trip?