If exactly 220 people sign up for a charter flight, Leisure World Travel Agency charges $282/person. However, if more than 220 people sign up for the flight (assume this is the case), then every fare is reduced by $1 times the number of passengers above 220. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 220. Show that the revenue function R is given by R(x)

Answer:251 passengers will result in a maximum revenue.Step-by-step explanation:The price per ticket of the first 220 passengers is given by:[tex]220*(282-x)[/tex]The price per ticket of the additional x passengers is:[tex]x(282 - x)[/tex]Adding both parts gives us the revenue function R(x):[tex]R = 220*(282 -x) + x(282-x)[/tex]The term (282-x) is present in both parts and can be factored:[tex]R(x)= (220+x)*(282-x)\\R(x)= -x^2 +62x+ 62,040[/tex]To find how many passengers will result in a maximum revenue, derive the function R(x) and find its zeroes:[tex]\frac{d}{dx}R(x)= \frac{d}{dx} (-x^2 +62x+ 62,040)\\\frac{d}{dx}R(x)=-2x +62 = 0\\x=\frac{62}{2}\\x=31[/tex]31 passengers above 220 will result in a maximum revenue. Therefore, 251 passengers will result in a maximum revenue.