SOLUTION: I'm totally lost and frustrated with these questions. 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

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: I'm totally lost and frustrated with these questions. 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       Log On

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Question 464162: I'm totally lost and frustrated with these questions. 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
As the number of TV’s produced increases, what happens with the profit?
How do you know how many solutions there are to the function? Show how you determined the nature of the solutions using the Discriminant.
Find the solutions and explain what these solutions represent. Use the Quadratic Formula.
How many TV’s must be produced to reach a minimum or maximum profit? Show your work in detail.
What is this minimum or maximum profit? Show your work in detail.
What is the vertex of this graph? Describe what this point represents for this function.
Provide a graph of this function. Include solutions (roots), vertex, axis of symmetry, and labels for each.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

 p(x) =  -x^2 + 812x - 9600 (graphically represents parabola opening downward



As the number of TV’s produced increases, what happens with the profit? 

 profit declines after the maximum profit is reached

How do you know how many solutions there are to the function? quadratic 2 sol.

Show how you determined the nature of the solutions using the Discriminant. 

    Positve value for discriminant:  real solutions

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-812+%2B-+sqrt%28+620944%29%29%2F%28-2%29+

   x = (-812 ± 788)/-2

   x =  1600/2 = 800

   x =   24/2 = 12  Zero profit at 12 units and 800 units

How many TV’s must be produced to reach a maximum profit? 

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

 P(x) =  -x^2 + 812x - 9600 

 P(x) = -(x-406)^2 + 164836 - 9600  |completing the square

Vertex is at(406,155,236) the maximum point for the parabola. 

 maximum profit of 155,236 at 406 units produced.