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Thread: standard form

  1. #1
    Senior Member euclid2's Avatar
    May 2008
    Ottawa, Canada

    standard form

    I know this is a long question and I have atempted it, although i just really dont have a clue unfortunately

    After a few calculations, Allison and Hannah realize the park will make more money if they raise the price of admission. However, they also understand that there must be a limit to how much the park can charge. As a result, they model the situation with the equation, R = (2400 - 80x)(8 + 0.5x), where R represents the revenue from sales and x represents the number of price increases.

    1. Write this equation in standard form, R = ax2 + bx + c. Show all of the steps leading to the final answer.
    2. What price should the park charge to maximize its revenue?
    3. What price range would produce a revenue over $20,000?
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  2. #2
    Jul 2008
    Use FOIL to expand the two binomials. Look here for reference Using FOIL - Free Math Help
    You should get $\displaystyle R={-40x^{2}+560x+19200}$

    Notice that the function is a parabola opening down. So as $\displaystyle x\to\pm\infty$, $\displaystyle R\to\pm\infty$.
    Thus you need to find the vertex to get the highest R value. Use the formula $\displaystyle x={\dfrac{-b}{2a}}={\dfrac{-(560)}{2(-40)}}$.

    Set the equation, $\displaystyle =-40x^{2}+560x+19200>20000$ and solve for x.
    You should get something like $\displaystyle x < -\left(\sqrt{69}+7\right)$ or $\displaystyle x>\sqrt{69}-7$ as the range.
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