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Quadratic function profits

  1. Feb 26, 2009 #1
    1. The problem statement, all variables and given/known data
    It Costs a bus company $225 to run a minibus on a ski trip, plus $30 per passenger. the bus has seating for 22 passengers, and the company charges $60 per fare if the bus is full. For each empty seat, the company has to increase ticket price by $5. How many empty seats should the bus run with to maximize profit from this trip?


    2. Relevant equations
    vertex form
    factored form
    standardform
    cost function
    revenue function
    profit function

    The back of the book says 8 empty seats
    3. The attempt at a solution
    my equations
    C(x)=(225+30x)
    R(x)=(60-5x)
    P(x)=R(x)-C(x)
    So far ive tried doing the equations numerus ways, ive tried multiplying the terms together, doesn't work I think it gave me 3 empty seats. Tried using the profit functions above, still doesn't give me 8 empty seats. I'm guessing it is either one of my functions that is incorrect but im not sure which
     
    Last edited: Feb 26, 2009
  2. jcsd
  3. Feb 26, 2009 #2

    symbolipoint

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    You formulated the Rate ( R(x) ) incorrectly. View the passenger rate as Dollars Per Passenger. The company charges 60 dollars per fare if bus is full, or bus takes 22 passengers. How much money is that? 60 dollars per fare multiplied by 22 fares. Now, what happens for each decrement of 1 passenger? This is where you became stuck(?).
    Why did you subtract instead of add? Best I could tell, you want R(x)=60+5x, because "increase ticket price by $5 for each empty seat". x=[count of passengers]
     
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