SOLUTION: The demand equation for a certain type of printer is given by: D = -200p + 35,000 The supply equation is predicted to be: S = -p^2 + 400p - 20,000 Find the equilibrium price.

Algebra ->  Radicals -> SOLUTION: The demand equation for a certain type of printer is given by: D = -200p + 35,000 The supply equation is predicted to be: S = -p^2 + 400p - 20,000 Find the equilibrium price.       Log On


   

Question 65747: The demand equation for a certain type of printer is given by:
D = -200p + 35,000
The supply equation is predicted to be:
S = -p^2 + 400p - 20,000
Find the equilibrium price.
This question has me completely lost on how to start, middle, end, or answer. Hope there is some help out there for this one. Thank you very very much
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
When your supply meets (=) the demand, you have fulfilled equillibrium.
Supply = Demand
-p^2 + 400p - 20,000 = -200p + 35,000
0 = p^2 - 600p + 55,000
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ap%5E2%2Bbp%2Bc=0 (in our case 1p%5E2%2B-600p%2B55000+=+0) has the following solutons:

p%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-600%29%5E2-4%2A1%2A55000=140000.

Discriminant d=140000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--600%2B-sqrt%28+140000+%29%29%2F2%5Ca.

p%5B1%5D+=+%28-%28-600%29%2Bsqrt%28+140000+%29%29%2F2%5C1+=+487.082869338697
p%5B2%5D+=+%28-%28-600%29-sqrt%28+140000+%29%29%2F2%5C1+=+112.917130661303

Quadratic expression 1p%5E2%2B-600p%2B55000 can be factored:
1p%5E2%2B-600p%2B55000+=+1%28p-487.082869338697%29%2A%28p-112.917130661303%29
Again, the answer is: 487.082869338697, 112.917130661303. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-600%2Ax%2B55000+%29