Ashley L.
asked • 05/24/22A group of people wish to charter a boat. The fee is $1000 per person for the first 100 people, but decreases by $5 (for everyone) for each person beyond 100. The charter company will have costs of $40000 +200n, where n is the number of people on the trip. If the boat’s capacity is 250, what number of passengers will maximize the company's profits?
Stanton D. answered • 05/24/22
Tutor to Pique Your Sciences Interest
Hi Ashley L.,
You MIGHT view this as a calculus problem. But you don't need to -- just balance the charge/person (which is a linearly descending function of n) with the marginal cost/passenger (200n). When they balance, if that is within n<=250, that's your maximal profit point. That's algebra, by the way.
-- Cheers, --Mr. d.
Get a free answer to a quick problem.
Most questions answered within 4 hours.
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Answers · 3
Answers · 7
Answers · 3
Answers · 8
Answers · 4
AJ N.
5.0 (1,300)
Justin C.
5.0 (1,065)
Ephraim J.
5.0 (3,078)
Stanton D.
I might have understated the complexity of setting up the revenue. Basically, it's 1000n - 5(n-100) for n>=100. That's 500+995n , isn't it. The charge per person is descending, but the total revenue is ascending. There's also another important financial consideration in problems of this sort: disaster insurance coverage if you're cruising into the "Bermuda Triangle". Look the term up, if you've never encountered it before!05/24/22