Maximum profit?

Question

The profit of a video company, in thousands of dollars, is given by P(x)= -5x^2+550x-5000, where x amount of spent on advertising in thousands of dollars;
a)determine the maximum profit that the company can make.
b)determine the amounts spent on advertising that will result in a profit.
c) Detdetermine the amount spent on advertising that will result in a profit of at least $4 000 000.

Answer 1

This is a math question, not a business question. Anyway ...

a) $10,125,000
b) Between $10,000 and $100,000 will result in a profit
c) From $20,000 to $90,000 (inclusive) will result in a profit of at least $4,000,000.

Answer 2

This doesn't have an answer as required, reason,
the first derivative is
-10x+550. So the profit is maximum when x=55 and it cannot have value in thousands, in which case you will have losses.
Substituting 55 for x in the profit equation given you will get the maximum profit which is
-5x55^2+550x55-5000=10125.
This is the maximum profit possible according to the equation given. I don't know how the other guy got the answer like the above, since any value greater than or less than 55 will produce suboptimal results. So since this is the case other parts are irrelevent.