Question

A local club is arranging a charter flight. The cost of the trip is $360 each for 90 passengers, with a refund of $2 per passenger for each seat sold in excess of 90. (Hint: x=number of passengers over 90.)

a.) Write the revenue function R(x).
b.) Find the maximum revenue and the number of passengers which will maximize the revenue. Be sure to show all necessary supporting calculus.

Answer 1

A.
`R(x)=(360-2x)(90+x)\\R(x)=32400+360x-180x-2x^2\\R(x)=-2x^2+180x+32400`

B.
`R(x)=-2x^2+180x+32400\\R'(x)=-4x+180=0\\180=4x\\45=x\\\\R(45)=-2(45)^2+180(45)+32400\\R(45)=-2(2025)+8100+32400\\R(45)=-4050+40500\\R(45)=36450\\\\90+45\\135`

135 passengers will maximize the revenue at $36,450.