Question 54313: Mona Kalini gives a walking tour of honolulu to one person for $47. To increase her business, she advertised at the national honolulu orthondontist convention that she would lower the price by $1 per person for each additional person, up to 47 people. Write her revenue as a function of the number of people on the tour. What number of people on the tour would maximize her revenue? What is the maximum revenue for her tour?
Answer by jenrobrody(19)   (Show Source):
You can put this solution on YOUR website! x = number of people on the tour
48-x = price per person for x number of people,
for example one person(x=1) would give 48-1=47 dollars per person
or 10 people(x=10) would give 38 dollars per person
The revenue earned would be the cost per person times the number of people.
R(x)=(48-x)x or R(x)=48x-x^2
Written in standard form: R(x)= -1x^2 + 48x + 0 a=-1, b=48, c=0
Vertex(min/max) at x = -b/2a = -48/(2*-1)=-48/-2 = 24
Maximum revenue for 24 people.
R(24)=(48-24)(24) = 24(24) = 570
|
|
|
