Answer :
Answer:
$310.
Step-by-step explanation:
We have been given that the price p of bolts is related to the quantity q that is demanded by [tex]p = 620-4q^2[/tex] where q is measured in hundreds of bolts. Suppose the supply function for bolts is given by [tex]p = 4q^2[/tex], where q is the number of bolts (in hundreds).
We know that equilibrium price is the point where demanded quantity is equal to supplied quantity.
To solve our given problem, we will equate demand function with supply function and demand function as:
[tex]4q^2=620-4q^2[/tex]
[tex]4q^2+4q^2=620-4q^2+4q^2[/tex]
[tex]8q^2=620[/tex]
[tex]\frac{8q^2}{8}=\frac{620}{8}[/tex]
[tex]q^2=77.5[/tex]
Now, we will substitute [tex]q^2=77.5[/tex] in equation [tex]p = 4q^2[/tex], we will get:
[tex]p = 4q^2\Rightarrow 4(77.5)=310[/tex]
Therefore, the equilibrium price would be $310.
