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.

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Question 90296This question is from textbook Beginning Al
: 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.
No clue on what to do...help is appreciated! This question is from textbook Beginning Al

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
To find the equilibrium price, set D equal to S


Add to both sides

Subtract from both sides

Add to both sides

Combine like terms



Now 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



Negate -600 to get 600



Square -600 to get 360000



Multiply to get



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



Simplify the square root



Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or


which split up to


or


and simplify to


or


Which approximate to

or


So our solutions are:
or



However, since the first solution produces a negative demand value, we must discard the first solution.

So the equilibrium price is $112.92
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