document.write( "Question 464162: I'm totally lost and frustrated with these questions. Please help!
\n" ); document.write( "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 \r
\n" ); document.write( "\n" ); document.write( "As the number of TV’s produced increases, what happens with the profit?\r
\n" ); document.write( "\n" ); document.write( "How do you know how many solutions there are to the function? Show how you determined the nature of the solutions using the Discriminant.\r
\n" ); document.write( "\n" ); document.write( "Find the solutions and explain what these solutions represent. Use the Quadratic Formula.\r
\n" ); document.write( "\n" ); document.write( "How many TV’s must be produced to reach a minimum or maximum profit? Show your work in detail.\r
\n" ); document.write( "\n" ); document.write( "What is this minimum or maximum profit? Show your work in detail.\r
\n" ); document.write( "\n" ); document.write( "What is the vertex of this graph? Describe what this point represents for this function.\r
\n" ); document.write( "\n" ); document.write( "Provide a graph of this function. Include solutions (roots), vertex, axis of symmetry, and labels for each.
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Algebra.Com's Answer #317949 by ewatrrr(24785) $\"\"$ $\"About$

You can put this solution on YOUR website!

 
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document.write( "Hi,
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document.write( " p(x) =  -x^2 + 812x - 9600 (graphically represents parabola opening downward\r
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document.write( "As the number of TV’s produced increases, what happens with the profit? 
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document.write( " profit declines after the maximum profit is reached
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document.write( "How do you know how many solutions there are to the function? quadratic 2 sol.
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document.write( "Show how you determined the nature of the solutions using the Discriminant. 
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document.write( "    Positve value for discriminant:  real solutions
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document.write( "   x = (-812 ± 788)/-2
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document.write( "   x =  1600/2 = 800
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document.write( "   x =   24/2 = 12  Zero profit at 12 units and 800 units
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document.write( "How many TV’s must be produced to reach a maximum profit? 
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document.write( "Using the vertex form of a parabola,  where(h,k) is the vertex
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document.write( " P(x) =  -x^2 + 812x - 9600 
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document.write( " P(x) = -(x-406)^2 + 164836 - 9600  |completing the square
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document.write( "Vertex is at(406,155,236) the maximum point for the parabola. 
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document.write( " maximum profit of 155,236 at 406 units produced.  \n" );
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