SOLUTION: 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

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
RELATED QUESTIONS
A charter flight charges a fare of $300 per person plus $6 per person for each... (answered by ankor@dixie-net.com)

For a trip to a resort, a charter bus company charges a fare of $48 per person plus $2... (answered by ewatrrr)

For a trip to a resort, a charter bus company charges a fare of $48 per person plus $2... (answered by josgarithmetic)

An airline carries 180 passengers and 10 tonnes of freight and earns $75000 for its... (answered by nerdybill)

A charter company will provide a plane for a fare of $200 each for 80 or fewer... (answered by stanbon)

A taxi cab company charges each person a flat fee of $1.85 plus an additional $.40 per... (answered by checkley77)

a charter company will provide a plane for a fare of $200 each for 80 or fewer... (answered by drk)

A plane with 150 seats may be chartered for$240 per person plus a fee of $6 per person... (answered by josmiceli)

The revenue of a charter bus company depends on the number of unsold seats. IF 100 seats (answered by ewatrrr)