SOLUTION: The demand equation for a certain printer is given by D = -200p +35,000 The supply equation is predicted to be S = -p^2+ 400p

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Question 121757: The demand equation for a certain 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?
I just need some help on how to start this problem.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
The equilibrium price occurs when the demand (D) equals the supply (S). In other words, when

Set the two equations equal to each other. Now let's solve for p

Add 200p to both sides. Subtract 35000 from both sides.

Combine like terms

Let's use the quadratic formula to solve for p:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-1, b=600, and c=-55000

Square 600 to get 360000

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So the possible solutions are:
or

However, when you plug in into the equations, you get a negative number (which does not make sense). So our only solution is

Now round to the nearest hundredth

So the equilibrium price is $112.92

SOLUTION: The demand equation for a certain 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? I jus