Question

A charter company will provide a plane for a fare of $60 per person for 20 passengers. For each passenger in excess of 20, the fare is decreased $2 per person for everyone. Use this to help determine the ideal number of passengers that will maximize the charter company's revenue. Set up an equation in (cost)*(product) that represents this situation.

Answer 1

25

Step-by-step explanation:

Let number of passengers greater than 20 be 'x'

thus,

the total number of passengers = 20 + x

and,

the total cost = $60 - $2x

now,

The revenue function will become as:

R(x) = cost × Number of passengers

or

R(x) = ( 60 - 2x ) × ( 20 + x )

or

R(x) = 1200 + 60x - 40x - 2x²

or

R(x) = 1200 + 20x - 2x²

Now,

for point of maxima, differentiating w.r.t 'x'

we have

R'(x) = 20 - 4x = 0

or

x = 5

Hence,

the ideal number of passenger is 20 + x = 20 + 5 = 25