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Math Help - Business Calculus help

  1. #1
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    Business Calculus help

    The owner of a luxury motor yacht charges $500/person/day if exactly 15 people show up for the cruise. However, if more than 15 people sign everyone's fare is reduced by $3 for each additional passenger. Assume that at least 15 people sign up for the cruise.

    A) Find the revenue function.
    B) What is the number of people that will result in the maximum revenue?
    C) What is the maximum revenue?
    D) What is the fare per person in this case?

    Please show work if you can. Really need some help with this one. Thanks!!
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  2. #2
    MHF Contributor

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    Re: Business Calculus help

    Do you not know the meanings of any of these words? If, for example, you know what "revenue function" means, this problem should be easy. If not where did you get this problem?
    The crucial point is that "15 people" isn't it? Suppose there are 16 people. Then there is 1 "additional passenger" so everyone's fare is reduced by $3. That means every one's fare is now 500- 3= $497. The "revenue" is 497(16)= $7952. Suppose there are 17 people. Then there are 17- 15= 2 "additional passengers" so every one's fare reduced by 3(2)= $6, from $500 to 500- 6= $494. The revenue is 17(494).

    What you want to do is go through that reasoning "in general" (which is, really, the whole point of algebra!). If there are "P" people, then there are P- 15 "additional passengers" so everyone's fare is reduced by 3(P- 15). That is, everyone pays 500- 3(P- 15). If P people each pay 500- 3(P- 15) dollars, what is the total revenue?
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