Question 890205: For a charter flight, an airline charges a fare of $180 per person plus $10 per person for each unsold seat on the plane. If the plane holds 100 passengers and if x represents the number of unsold seats,
(i) find an expression for the total revenue received for the flight.
(ii) Find the maximum number of unsold seats that the plane can have
(iii) Hence find the maximum revenue for the flight.
[Hint: To find an expression for the total revenue, multiply the number of people flying, by the price per ticket.]
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For a charter flight, an airline charges a fare of $180 per person plus $10 per person for each unsold seat on the plane. If the plane holds 100 passengers and if x represents the number of unsold seats,
(i) find an expression for the total revenue received for the flight.
let x=number of unsold seats
100-x=number of seats sold
fare price=(180+10x)
Revenue= fare price*number of seats sold=(180+10x)(100-x)
R=18000+1000x-180x-10x^2
R=-10x^2+820x+18000=0
R=-x^2+82x+1800
complete the square:
R=-(x^2-82+41^2)+41^2+1800
R=-(x-41)^2+3481
This is an equation of a parabola that open down with vertex at (41,3481)
..
(ii) Find the maximum number of unsold seats that the plane can have
maximum number of unsold seats that the plane can have=100
...
(iii) Hence find the maximum revenue for the flight.
maximum revenue for the flight=$3,481 when 41 seats are sold
|
|
|
