SOLUTION: Please help with this word problem. The demand equation for a certain type of printer is given by D = -200p + 35000 The supply equation is predicted to be S = -p^2 + 400p - 2

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Question 42476: Please help with this word problem.
The demand equation for a certain type of printer is given by
D = -200p + 35000
The supply equation is predicted to be
S = -p^2 + 400p - 20000
Find the equilibrium price.
Thanks!!
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
The demand equation for a certain type of printer is given by
D = -200p + 35000 or y = -200p + 35000
The supply equation is predicted to be
S = -p^2 + 400p - 20000 or y = -p^2 + 400p - 20000
So ....
y = -p^2 + 400p - 20000
-200p + 35000 = -p^2 + 400p - 20000
0 = -p^2 + 600p - 55000
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=140000 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 112.917130661303, 487.082869338697. Here's your graph:
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