# Help again, largest revenue and weekly profit

• Dec 7th 2009, 09:46 AM
maria
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 : )
• Dec 7th 2009, 05:19 PM
Scott H
For the first problem, if we call the revenue $\displaystyle R$, we have

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

Differentiating, we obtain

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

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

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