Question

I need help solving this problem
The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3770. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x

Answer 1

Okay, are you looking for the equation then, or is another part confusing you?

Answer 2

Yes I am looking for the equation and the least number of passengers it must carry in order to make a profit?

Answer 3

To find the equation, let "h" represent the hours, alright? So it makes $100 per hour (100 x h) and it costs $3770 per hour (3770 x h) to operate. Can you make the equation from there?

Answer 4

*Correction: $100 per customer, sorry. Let me recalculate that!

Answer 5

\[P=100c-3770h\] should be your equation. Also, you should note that: \[0 \le x \le 295\]

Answer 6

So by setting the hour to 1, you can solve for "c," which is how many customers it needs in one hour to be more than 3770! Let me know if you need anything else!

Answer 7

okay i did what you said and my teacher told me that I have to find f(x) instead of the equation

Answer 8

sorry the hourly profit not f(x)

Answer 9

To find the hourly profit, you would have to know exactly how many customers there are per hour. You know that to have any profit at all, the number of customers has to make 100 x c equal a number greater than 3770.

3770 is divisible by 100 so that you know there has to be at least 378 customers for there to be any profit. (Having exactly 377 customers would make P = 0, and you can't have half a customer!)