Question 84863
The demand and supply equations for a certain item are given by
D = –5p + 40
S = –p2 + 30p – 8
Find the equilibrium price.
:
Equilibrium price occurs when demand = supply
:
Which means D = S
:
Which means:
-5p + 40 = -p^2 + 30p - 8
:
Arrange all terms on the left:
+p^2 - 30p - 5p + 40 + 8 = 0
:
p^2 - 35p + 48 = 0; a not-so-friendly quadratic equation
:
Requires the quadratic formula to solve: a=1; b=-35; c=48
{{{p = (-(-35) +- sqrt( -35^2 - 4 * 1 * 48 ))/(2*1) }}}
{{{p = (+35 +- sqrt(1033 ))/(2) }}}
{{{p = (+35 + 32.14)/(2) }}}
{{{p = 67.14/2}}}
p = 33.57, 1st solution
and
{{{p = (+35 - 32.14)/(2) }}} 
{{{p = 2.86/2}}}
p = 1.43; 2nd solution
:
The 1st solution does not make sense, substitute in the demand equation,
-5(33.57) + 40  gives a negative value