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

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

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.