Answer:
When the price is approximately $92.35, the demand and supply are equal.
Step-by-step explanation:
The given functions are
[tex]S(p)=400-4p+0.00002p^{4}\\ D(p)=2800-0.0012p^{3}[/tex]
Where [tex]S(p)[/tex] represents the supply, [tex]D(p)[/tex] represents the demand and [tex]p[/tex] the price.
So, to determine the price for which the supply equals the demand, we just need to use the given functions as,
[tex]S(p)=D(p)\\400-4p+0.00002p^{4}=2800-0.0012p^{3}[/tex]
Then, we solve for [tex]p[/tex]
[tex]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[/tex]
So, using a calculator, we have
[tex]p\approx 92.35\\p\approx -123.58[/tex]
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.
