calculus

posted by .

With x people on board, a South African airline makes a profit of (1104 − 3 x) rands per person for a specific flight.
A. How many people would the airline prefer to have on board?
Answer: x=
B. What is the maximum number of passengers that can board such that the airline still profits?
Answer: x=

  • calculus -

    If the profit is (1104-3x) per person, then the total
    profit = x(1104-3x) = 1104x - 3x^2

    d(profit)/dx = 1104 - 6x
    = 0 for max profit
    6x = 1104
    x = 184 , (max profit = 101568)

    To have any profit
    x(1104-3x) > 0
    critical values are x=0 or x=368

    so min number of passengers is 1 for a profit of 1101, max number of passengers is 367 for a profit of 1101

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. statistics

    an airline estimates that 97%of people booked on their flights actually show up.if the airline books 70 people on a flight for which the maximum number is 68,what is the probability that the number of people who show up will exceed …
  2. Stats

    An airline estimates that 91% of people booked on their flights actually show up. If the airline books 80 people on a flight for which the maximum number is 78, what is the probability that the number of people who show up will exceed …
  3. STAT

    Airline overbooking is a common practice. Many people make reservations on several flights due to uncertain plans and then cancel at the last minute or simply fail to show up. Eagle Air is small commuter airline. Their planes hold …
  4. math

    using past data, an airline believes that 8% of the people who make reservation for a particular flight will not appear. for this flight, the seating capacity is 300 passengers and the airline sells 315 tickets. what is the probability …
  5. probability

    For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there …
  6. Probability

    For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there …
  7. Probability

    For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there …
  8. math

    An airline’s weekly flight data showed a 98% probability of being on time. If this airline has 15,000 flights in a year, how many flights would you predict to arrive on time?
  9. Math

    An airline believes that the probability of a passenger being a no-show on a morning flight is 12%. If the airline overbooks a 300 seat morning flight by selling 350 tickets how many empty seats should the airline expect to have on …
  10. math

    an airline company offers a round-trip group flight from New York to London. If x people sign up for the flight, the cost of each ticket is to be 1000-2x dollars. Find the maximum revenue the airline company can receive from the sale …

More Similar Questions