SOLUTION: an outdoor adventure company advertises that they will, provide a guided mountain bike trip and a picnic lunch for $50 per person. they must have a guarantee of 30 people to do the
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Question 1132533: an outdoor adventure company advertises that they will, provide a guided mountain bike trip and a picnic lunch for $50 per person. they must have a guarantee of 30 people to do the trip. furthermore, they agree that for each person in excess of 30, they will reduce the price per person for all riders by $0.50. how many people will it take to maximize the company’s revenue
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
n outdoor adventure company advertises that they will, provide a guided mountain bike trip and a picnic lunch for $50 per person.
they must have a guarantee of 30 people to do the trip. furthermore, they agree that for each person in excess of 30, they will reduce the price per person for all riders by $0.50.
how many people will it take to maximize the company’s revenue
:
let x = no. of persons over 30 and = no. $.50's reduction in price
:
Revenue = no. of people * price
R(x) = (30 + x)(50-.5x)
FOIL
R(x) = 1500 - 15x + 50x - .5x^2
R(x) = 1500 + 35x - .5x^2
A quadratic equation
R(x) = -.5x^2 + 35x + 1500
max revenue occurs on the axis of symmetry, x = -b/(2a), where
a = -.5, b b = 35
x =
x = 35
:
Find no. over 30: 30 + 35 = 65 people will maximize revenue
:
Find cost per person: 50 -.5(35) = $32.50
Max revenue: 65 * 32.5 = $2112.50
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