Suppose that the demand and supply for artificial Christmas

Suppose that the demand and supply for artificial Christmas trees is given by the functions below where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price. p = 107.10-0.30q (demand function) p = 0.01 q2 + 5.31 (supply function) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The equilibrium price of $ gives a demand that is equal to a supply of hundred trees. (Simplify your answer. Type integers or simplified fractions.) The equilibrium price does not exist.

Solution

p = 107.10 - 0.30q

and p = 0.01q^2 + 5.31

Then 0.01q^2 + 5.31 = 107.10 - 0.30q

0.01q^2 + 0.30q - 101.79 = 0

q = 87 (q = -117 is not possible)

Then p = 107.10 - 0.3*87 = 81

So, price = p = $81

Quantity of trees = q = 8700