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.
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)
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(ii) Find the maximum number of unsold seats that the plane can have
 maximum number of unsold seats that the plane can have=100
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(iii) Hence find the maximum revenue for the flight. 
maximum revenue for the flight=$3,481 when 41 seats are sold