Charter Revenue The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $592/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 100) for the cruise, then each fare is reduced by $4 for each additional passenger.
Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht.
__ passengers
What is the maximum revenue?
What would be the fare/passenger in this case? (Round your answer to the nearest dollar.) dollars per passenger
so, we know that if 20+x people sign up, the revenue is
r(x) = (20+x)(592-4x) = 4(20+x)(148-x)
From Algebra I, we know that the vertex of that parabola is midway between the roots, at x = 64, so max revenue is r(64) = 28,224
But, since this is for a calculus class,
r(x) = -4(x^2 - 128x - 2960)
dr/dx = -4(2x-128) = -8(x-64)
dr/dx = 0 at x = 64, as above
so there will be 84 passengers at $336 each