SOLUTION: I submitted this earlier, but have not seen this answered yet. I got $58.58 and $341.42 but cannot get the numbers to check. I think I am doing the demand problem incorrectly....

Algebra ->  Radicals -> SOLUTION: I submitted this earlier, but have not seen this answered yet. I got $58.58 and $341.42 but cannot get the numbers to check. I think I am doing the demand problem incorrectly....      Log On


   



Question 42812: I submitted this earlier, but have not seen this answered yet. I got $58.58 and $341.42 but cannot get the numbers to check. I think I am doing the demand problem incorrectly....HELP.
The demand equation for a certain type of printer is given by
D= -200p + 35,000
The supply equation is predicted to be
S= -p2 + 400p - 20,000
Find the equilibrium price.

-200p + 35,000 = -p2 + 400p - 20,000
-p2 - 400p - 20,000 = 0
a = 1 b = -400 c = 20,000
D = - 200(58.58) + 35,000 = -11,716 + 35,000
= 23,284
S= -(58.58)2 + 400(58.58) - 20,000
D = - 200(341.42) + 35,000 = -68284 + 35,000
= 33284
S= -(341.42)2 + 400(341.42) - 20,000


Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Price will be in equilibrium when demand is equal to supply.

So for equilibrium price, D = S i.e. -200p+%2B+35000+=+-p%5E2+%2B+400p+-+20000
or p%5E2+-+600p+%2B+55000+=+0.

To find the equilibrium price we have to solve the above quadratic equation
p%5E2+-+600p+%2B+55000+=+0.
Applying quadratic formula,
p+=+%28-%28-600%29+%2B-+sqrt%28+%28-600%29%5E2-4%2A1%2A55000+%29%29%2F%282%2A1%29+
or p+=+%28600+%2B-+sqrt%28360000+-+220000%29%29%2F2+
or p+=+%28600+%2B-+sqrt%28140000%29%29%2F2+
Either p = 487.08 or p = 112.92

Hence $487.08 and $112.92 are the two values of equilibrium prices.