Hello kaebun:
The place to start is understanding the question.
When they talk about the equilibrium price, they are talking about the price where supply equals demand.
You have formulas for both the supply and demand, so set them equal to one another:
6 + 0.001 * p^3 = 80 - 0.02 * p^2
Do you know how to solve an equation like this? Remember, the variable 'p' represents the price. Once you've solved this equation, you will have the equilibrium price.
Then calculate either the supply or the demand by inputing this solution for p into either of the given functions to find the number of hair dryers.
I'll get you started on solving the equation; let us know if you need more help on this problem.
Start by getting all of the terms on one side of the equation and zero on the other side.
Add 0.02 * p^2 to both sides.
Subtract 80 from both sides.
This gives you:
0.001 * p^3 + 0.02 * p^2 - 74 = 0
The coefficients all share 0.001 as a factor, so factor it out:
0.001 * (p^3 + 20 * p^2 - 74000) = 0
Divide both sides by 0.001 to eliminate this factor from the equation:
p^3 + 20 * p^2 - 74000 = 0
Can you take it from here? Again, let us know if you still need help.
By the way, if you have a graphing calculator, graph the following:
y1 = x^3 + 20 * x^2 - 74000
Set the window so x goes from 0 to 50 and y goes from 0 to 60000. The x-intercept corresponds to the equilibrium price 'p'.
~ Mark
