Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: S(p) = 400 - 4p + 0.00002p4 and D(p) = 2800 - 0.0012p3, where p is the price. Determine the price for which the supply equals the demand.

Question

anonymous · Answer

Supply equals demand for the $p$ value that makes
$$\begin{align*}S(p)&=D(p)\
400-4p+0.00002p^4&=2800-0.0012p^3\end{align*}$$
Judging by the coefficients and powers of $p$, can I assume you can use a calculator for this one?

anonymous · Answer

Yeah what would you like me to type in ?

anonymous · Answer

Do you have a graphing calculator? Or at least some online one? All you really need to do is solve the following equation for $p$:
$$0.00002p^4+0.0012p^3-4p-2400=0$$
Unless there's some way to factor that? I'm not sure yet.

anonymous · Answer

Yeah I have one

anonymous · Answer

Is there a way to put p in to the calculator

anonymous · Answer

I would just use WolframAlpha: http://www.wolframalpha.com/input/?i=0.00002p%5E4%2B0.0012p%5E3-4p-2400%3D0 Ignore the negative solution, since the price is assumed to be positive.