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26 July, 21:55

The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model shown below.

P = 190 + 80x - 0.5x^2

What expenditure for advertising will yield a maximum profit?

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  1. 26 July, 22:09
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    The profit:

    P = - 0.5 x² + 80 x + 190

    The maximum profit will be at the vertex:

    x = - b / 2 a = - 80 : (2 * ( - 0.5)) = - 80 : ( - 1) = 80 (in hundreds of dollars)

    Answer:

    The amount of money that will yield a maximum profit is $8,000.
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