SOLUTION: hello i submitted these questions and get answer but what i needed to know was HOW do we get the answers I want to see the work so i learn, so i am resubmitting hoping for this: I

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: hello i submitted these questions and get answer but what i needed to know was HOW do we get the answers I want to see the work so i learn, so i am resubmitting hoping for this: I      Log On


   

Question 357524: hello i submitted these questions and get answer but what i needed to know was HOW do we get the answers I want to see the work so i learn, so i am resubmitting hoping for this:
I have been working on this all week and I just cannot get it. I know this is short notice but it is due with in the next 12 hours PLEASE HELP!
A plasma TV company determines that its total profit on the production and sale of x TVs is given by: P(x)= -x^2+812x-9600
the question that i am stuck on are as follows, and i have to show the work:
1. Find the solutions and explain what these solutions represent.
2. How many TV�s must be produced to reach a minimum or maximum profit?
3.What is this minimum or maximum profit?
4.What is the vertex of this graph? How is this point related to your answers from e and f?
I also have to graph this function. Include solutions (roots), vertex, axis of symmetry, and labels for each.

Thanks in advance
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
1. find the roots by setting P(x) equal to zero ___ -x^2 + 812x - 9600 = 0
___ dividing by -1 ___ x^2 - 812x + 9600 = 0
___ factoring ___ (x - 12)(x - 800) = 0
___ the roots are 12 and 800
___ the lower number represents the break even point where the costs equal the sales
___ the higher number probably represents market saturation (I do math, not finance)
to much product for the market and the price declines (and/or sales drop), causing profits to fall

2. the min (or max, in this case) lies midway between the roots (their average)
___ (800 + 12) / 2 = 406

3. plug 406 into the profit function ___ P(406) = -406^2 + 812(406) - 9600

4. the x-coordinate of the vertex is 406 , the y-coordinate is the answer from #3
___ this represents the max profit and the number of sets needed to achieve it


the axis of symmetry passes through the vertex
___ it is a vertical line whose equation is ___ x = 406


the parabola opens downward
it passes through the roots and the vertex (which is the "nose" of the parabola)
the axis of symmetry is the midline of the parabola