SOLUTION: The demand and supply equations for a certain item are given by D = �5p + 40 S = �p2 + 30p � 8 Find the equilibrium price.

Question 88322: The demand and supply equations for a certain item are given by
D = �5p + 40
S = �p2 + 30p � 8
Find the equilibrium price.

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The equilibrium price occurs when supply equals demand. So the equilibrium price can be found by setting each equation equal to each other

Let the supply equal the demand

Add 5p to both sides

Subtract 40 from both sides

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=35, and c=-48

Square 35 to get 1225

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 approximate to

or

So our solutions are:
or

Notice when we graph (just replace p with x) we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer

So the equilibrium prices are 1.43 or 33.57
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The demand and supply equations for a certain item are given by
D = �5p + 40
S = �p2 + 30p � 8
Find the equilibrium price.
--------------------
Equilibrium means demand = supply
--------
-5p+40 = -p^2 + 30p - 8
p^2 - 35p + 48 = 0
p = [35+-sqrt(35^2-4*1*48)]/2
p = [35 +- sqrt(1033)]/2
p = $33.57 or p = $1.3
=================
Cheers,
Stan H.
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