Applications of Derivatives Question..? (1 Viewer)

[imoO]

Question:
An airline company marks the price of a flight at $400, less a group discount based on the number of bookings made. The price, R dollars for each person in the group of x people is R = 400 - 0.5x
The cost of running the flight is a fixed cost of $5000 plus $150 per person. Show that the profit on a flight of a group of x people is (250x - 0.5x^2 - 5000) dollars. Hence find the group size that maximises profit.



Comments:
I have no clue as to where to start. dy/dx=????

lol....

thanks in advance for help.

 

[tommykins]

Haha, you go to blackwattle - I'm guessing you know Anita? ANyways.

I'l be working on what's already given.

Profit for x amount of people = 250x - 0.5x^2 - 5000.

To maximise profit, you need to find the maximum TP of this fucntion.

y = 250x - 0.5x^2 - 5000
dy/dx = 250 - x

-x = -250

x = 250

a group of 250 will maximise profit.