The hourly operating cost of an airplane, which seats up to 405 passengers, is estimated to be $5,500. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the airplane as a function of the number of passengers x. (Be sure to specify the domain.)
What is the least number of passengers it must carry in order to make a profit? HINT [The cost function is constant (Variable cost = 0).]
Profit: P(x)=100x-5500
I solved it:
P(x)=0
100x-5500=0
5500/100=55 Passengers.
I don't understand what is wrong
Thank You
hourly revenue = 100p for p passengers
hourly cost = 5500
revenue=cost when
100p = 5500
p = 55
looks fine to me. why do you think it's wrong? anything over 55 passengers makes a profit, at $100/hr per extra passenger.
Because the purpose is to make a profit. So the passengers should be 56.
Well, let's see what went wrong there, my friend. It seems like you set the profit equation P(x) equal to zero, which is not correct. We want to find the least number of passengers needed to make a profit, not break even.
To find the minimum number of passengers needed to make a profit, we need to set the profit equation greater than zero:
P(x) > 0
100x - 5500 > 0
Now, let's solve for x:
100x > 5500
x > 55
So, the airline must carry more than 55 passengers in order to make a profit.
Therefore, the minimum number of passengers required to make a profit is 56, since it has to be an integer value.
Keep in mind that the domain for this scenario is x > 0, since we can't have a negative number of passengers.
Hope that clarifies things for you!
Your approach to finding the least number of passengers needed to make a profit is incorrect. Let me explain the correct method.
In the given problem, the hourly profit, P, earned by the airline operating the airplane is given by the formula:
P(x) = 100x - 5500,
where x represents the number of passengers.
To find the least number of passengers needed to make a profit, we need to set P(x) greater than zero, since profit is achieved when revenue exceeds costs.
Therefore, we solve the inequality P(x) > 0:
100x - 5500 > 0.
Now, let's solve this inequality:
100x > 5500,
x > 55.
Hence, the airline must carry more than 55 passengers to make a profit. Therefore, the least number of passengers it must carry in order to make a profit is 56.