x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. p = 83 − 4x2 and p = x2 + 15x + 33

Answer 1

83 - 4x^2 = x^2 + 15x + 33

0 = x^2 + 15x + 33 + 4x^2 - 83

0 = 5x^2 + 15x - 50

0 = x^2 + 3x - 10

0 = ( x + 5 )(x - 2 )

x+5=0 results in negative measures

x-2=0 ---> x = 2

at x = 2, or 2000 units, the demand price is

83 - 4*2^2 = 83 - 16 = $67

while the supply price is:

2^2 + 15(2)+33 = 4 + 30 + 33 = $67

so the equilibrium price is $67 and the ideal inventory is 2000 units