Question

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) = 2,800 - 0.0012p3, where p is the price. Determine the price for which the supply equals the demand.

Answer 1

S(p)=D(p)
400-4p+0.00002p4=2,800-0.0012p3
Solve for p
P=96.24

Answer 2

Answer:

When the price is approximately $92.35, the demand and supply are equal.

Step-by-step explanation:

The given functions are

$S(p)=400-4p+0.00002p^{4}\\ D(p)=2800-0.0012p^{3}$

Where $S(p)$ represents the supply, $D(p)$ represents the demand and $p$ the price.

So, to determine the price for which the supply equals the demand, we just need to use the given functions as,

$S(p)=D(p)\\400-4p+0.00002p^{4}=2800-0.0012p^{3}$

Then, we solve for $p$

$400-4p+0.00002p^{4}=2800-0.0012p^{3}\\400-4p+0.00002p^{4}-2800+0.0012p^{3}=0\\0.00002p^{4}+0.0012p^{3}-2400=0$

So, using a calculator, we have

$p\approx 92.35\\p\approx -123.58$

However, only the positive solution make sense to this problem, because we are looking for the price.

Therefore, when the price is approximately $92.35, the demand and supply are equal.