I hope my step-by-step guide will make this question easier to understand.
a) I start by just copying down the equation you gave me
P = - 0.3 x^2 + fx - m
now write 60 instead of f and write 1500 instead of m and you get
P = - 0.3 x^2 + 60x - 1500
That is all you have to do in the first part. Not too bad was it?
b) Now just write 50 instead of the number of awards x
and work out what P comes to.
This is just simple arithmetic so hopefully you will find it easy.
P = - 0.3 (50)^2 + 60(50) - 1500
P = - 0.3 (2500) + 3000 - 1500
P = - 750 + 1500 = 750
That means the profit is $750
c) The graph of a quadratic function is a parabola.
If that function is
ax^2 + bx + c
we are told it will have a maximum or a minimum when
2ax = -b or x = -b/2a
(You are not asked to explain why)
In this example b = 60, a = - 0.3
The minus before the 0.3 should tell you that the parabola is "upside down".
So it will have a maximum when x = -b/2a = (-60)/(-0.3) = 100
In words, the profit is a maximum when the number of awards, x, is 100.
d) Working out this part is just like b) but we write 100, (rather than 50), for x.
P = - 0.3 (100)^2 + 60(100) - 1500 = 7500
As always the method is far more important than the answer to an individual question.
So when you have copied it all out,
may I suggest that you cover the answers up,
and try to work it out again on your own.
Regards - Ian
