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Math Help - Help again, largest revenue and weekly profit

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    6

    Help again, largest revenue and weekly profit

    question again...

    i need some guidance to see if im doing this right

    -p^3 + 33p + 9
    First i did (pq) then i took the derivative to find revenue which i got
    -3p^2 +33p + 9p = 0 i need to find largest revenue with this equation

    well i keep getting to -p^2 = -11p -3

    is this right? or where do i go from here?

    Also i had to do a cost equation and had to find what -3p^2 + 18p -265 = 0 i need to find largest weekly profit with this equation

    I go to p^2= -88.3 + 6p

    Same question here, did i get the right numbers or of i did what do i do to solve?

    thank you : )
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  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    For the first problem, if we call the revenue R, we have

    R=pq=p(-p^3+33p+9)=-p^4+33p^2+9p.

    Differentiating, we obtain

    \begin{aligned}<br />
\frac{dR}{dp}&=\frac{d}{dp}(-p^4)+\frac{d}{dp}(33p^2)+\frac{d}{dp}(9p)\\<br />
&=-4p^3+33\cdot2p+9\cdot 1\\<br />
&=-4p^3+66p+9.<br />
\end{aligned}<br />

    For the second problem, we may use the Quadratic Formula:

    ax^2+bx+c=0\quad\Rightarrow\quad x=-\frac{b}{2a}\pm\frac{1}{2a}\sqrt{b^2-4ac}.
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