Could someone please answer this question: A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round trip fare of $20. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry
Please show your work, thank you!
Please show your work, thank you!
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Let P be the number of people that will take the trip. Let F be the fare in dollars. We are told:
P(20) = 500
ΔP/ΔF = -20/1 = -20
And so we have the point (20,500) and the slope -20, thus the point-slope formula gives us:
P - 500 = -20(F - 20)
P = -20F + 900
I suspect you are to maximize the revenue R, rather than the number of passengers. The revenue is the product of the number of people and the fare per person:
R = PF = -20F² + 900F = 20F(18 - F)
The vertex of this parabolic revenue function will be on the axis of symmetry with is midway between the roots, hence the fare that maximizes revenue is $9.
P(20) = 500
ΔP/ΔF = -20/1 = -20
And so we have the point (20,500) and the slope -20, thus the point-slope formula gives us:
P - 500 = -20(F - 20)
P = -20F + 900
I suspect you are to maximize the revenue R, rather than the number of passengers. The revenue is the product of the number of people and the fare per person:
R = PF = -20F² + 900F = 20F(18 - F)
The vertex of this parabolic revenue function will be on the axis of symmetry with is midway between the roots, hence the fare that maximizes revenue is $9.