SOLUTION: If p represents price per unit in dollars and q represents the number of units per unit of time, find the equilibrium point. Supply: p= (q+10)^2 , Demand: p=388-16q-q^2 With

Question 187638This question is from textbook mathematial analysis
: If p represents price per unit in dollars and q represents the number of units per unit of time, find the equilibrium point.
Supply: p= (q+10)^2 , Demand: p=388-16q-q^2
With details
Thank you, This question is from textbook mathematial analysis

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The equilibrium point is when supply and demand are equal.
.
Supply: p= (q+10)^2 , Demand: p=388-16q-q^2
.
Notice BOTH equation defines 'p'. Set them equal to each other then solve for 'q':
(q+10)^2 = 388-16q-q^2
Expanding the left side with FOIL:
(q+10)^2 = 388-16q-q^2
(q+10)(q+10) = 388-16q-q^2
q^2 + 20q + 100 = 388-16q-q^2
Move all terms to the left:
2q^2 + 20q + 100 = 388-16q
2q^2 + 36q + 100 = 388
2q^2 + 36q - 288 = 0
Divide both sides by 2:
q^2 + 18q - 144 = 0
Factoring the left:
(q+24)(q-6) = 0
.
q = {-24, 6}
A negative solution does not make sense so:
q = 6

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