# revenue problem

#### euclid2

An airline offers summer flights from toronto to london for groups of students. a minimum of 80 students must sign up for each flight, at a round-trip fare of $2400 per person. however, the airline will reduce the fare by$10 for each additional student who joins the flight. what number of passengers will give the airline the greatest revenue?

#### skeeter

MHF Helper
An airline offers summer flights from toronto to london for groups of students. a minimum of 80 students must sign up for each flight, at a round-trip fare of $2400 per person. however, the airline will reduce the fare by$10 for each additional student who joins the flight. what number of passengers will give the airline the greatest revenue?
let x = number of additional students

R(x) = (2400-10x)(80+x)

so, maximize R(x) ... remember the number of students is 80+x

euclid2

#### euclid2

let x = number of additional students

R(x) = (2400-10x)(80+x)

so, maximize R(x) ... remember the number of students is 80+x
so R(x)= -10x^2 + 1600x + 192000

R'(x)=-20x+1600 indicating a max

setting R'(x)=0

-20x+1600=0
-20x=-1600
x=80

where do i go from here?

#### euclid2

how do i finish the problem from here?

MHF Helper
HallsofIvy