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

Do you know how to star this problem?

anonymous · Answer

No

anonymous · Answer

If you were to plot these two, find where they intersect.

anonymous · Answer

They would intersect at x=96.24 and -118.26. Just chose the positive value.

anonymous · Answer

That would be were supply meets demand.

anonymous · Answer

Thank you

anonymous · Answer

You're welcome.

anonymous · Answer

How did they get this answer? :O @zepdrix

zepdrix · Answer

$$\Large\bf\sf S(p) \quad=\quad 400 - 4p + 0.00002p^4$$$$\Large\bf\sf D(p) \quad=\quad 2800 - 0.0012p^3$$And they want to know when:$$\Large\bf\sf S(p)\quad=\quad D(p)$$

zepdrix · Answer

$$\Large\bf\sf 400-4p+0.00002p^4\quad=\quad 2800-0.0012p^3$$Then we solve for p, right? :o

anonymous · Answer

:O! true true, and then just combine like terms and all? @zepdrix

zepdrix · Answer

Hmm so we don't have any like terms, except for the constants.
So moving some stuff around gives us:$$\Large\bf\sf 0.00002p^4+0.0012p^3-4p-2400\quad=\quad0$$

zepdrix · Answer

Hmmm

zepdrix · Answer

Why'd you ask about this question?
Did you have the same one come up in your class or something? :D

anonymous · Answer

I did this practice test (online classes) , and I'm reviewing, and I didn't get this one. So I'm all like :ssssssss

anonymous · Answer

xD ,So yeah, Like how would I solve this? Like can you help me step by step (with the math)

zepdrix · Answer

Hmm lemme see if I can figure this one out.
So we'll multiply by some really big number like 100,000
giving us:$$\Large\bf\sf 2p^4+120p^3-400,000p-240,000,000\quad=\quad0$$

zepdrix · Answer

That get's rid of the decimals.
So from here we can apply the Rational Root Theorem.

zepdrix · Answer

Hmm the numbers don't seem to work out nice and neat though :(
So I don't think that will work...

zepdrix · Answer

Hmm I dunno how you would solve this one.
There isn't a nice fancy "Quadratic Formula" for 4th order equations like this.

anonymous · Answer

hahahha, Yeah I tried too, but thanks anyways bro!

zepdrix · Answer

:3