Help on finding a function

whitewalt

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Sep 4, 2013
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Problem:
1. The owner of a luxury motor lot that sails among the 4000 greek islands charges $600 per person, per day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up for the cruise (up to the maximum capacity of 90) the fare for all passengers is reduced by $4.00 per person for each additional passenger. Assume that at least 20 sign up for the cruise, and lex x denote the # of passengers above 20.

a. Find a function R, giving the revenue per day realized from the charter.
b. What is the revenue per day if 60 people sign up?
c. What is the revenue per day if 80 people sign up?

To be clear, this is a survey of calculus class. I'm not asking you to do the problem for me, just asking for help on how to set up the function. Once I have the function, I believe I will be able to solve for parts b and c.

Thanks all,
W.
 
Problem:
1. The owner of a luxury motor lot that sails among the 4000 greek islands charges $600 per person, per day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up for the cruise (up to the maximum capacity of 90) the fare for all passengers is reduced by $4.00 per person for each additional passenger. Assume that at least 20 sign up for the cruise, and lex x denote the # of passengers above 20.

a. Find a function R, giving the revenue per day realized from the charter.
b. What is the revenue per day if 60 people sign up?
c. What is the revenue per day if 80 people sign up?

To be clear, this is a survey of calculus class. I'm not asking you to do the problem for me, just asking for help on how to set up the function. Once I have the function, I believe I will be able to solve for parts b and c.

Thanks all,
W.
The fare per person is ($600 - $4*x)
Total revenue is number of passengers (x) times fare per passenger.
. . .
 
The fare per person is ($600 - $4*x)
Total revenue is number of passengers (x) times fare per passenger.
. . .

Thank you for the response.

So the standard function relating to the problem would simply be f(x)=600-4x
a) f(60)= 600 - 4(60) = 360
b) f(80)= 600 - 4(80) = 280

Is this correct?
 
Thank you for the response.

So the standard function relating to the problem would simply be f(x)=600-4x
a) f(60)= 600 - 4(60) = 360
b) f(80)= 600 - 4(80) = 280

Is this correct?
No. The cost per passenger is what you called f(x).
Total revenue R = x*f(x), which will be a quadratic function.
 
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