SOLUTION: The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8 Find the equilibrium price. Please help. Thank you.

Question 33062: The demand and supply equations for a certain item are given by
D=-5p+40
S=-p^2+30p-8
Find the equilibrium price.
Please help. Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Equilibrium means D=S
So, -p^2+30p-8=-5p+40
p^2-35p+48=0
a=1, b=-35, c=48

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=1033 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 33.5701586799882, 1.4298413200118. Here's your graph:

Since item counts must be whole numbers, round
the values of "p" down to a whole number.
Hope this helps.
Cheers,
Stan H.
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