Question 280795
Business and Finance.
A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).

The demand equation for a certain type of printer is given by:

                      D= -200p + 35,000

The supply equation is predicted to be:

                      {{{S= -p^2 +400p - 20000}}}

A). Does the graph of the supply equation open up or down::::Down

How did you determine this:::The coefficient of p^2 is negative.
==================================================================

B). What is the point of the vertex of the supply equation?
x = -b/2a = -400/(-2) = 100 ; S(100) = -10000 + 40000 - 20000
= 10,000
Vertex: (100,10,000)
==================================================================

C). How many solutions are there to the supply equation? How do you know?
Ans: Two ; it is a quadratic.
===================================

D). Find the equilibrium price (Hint: The equilibrium price is the price for which supply equals demand).
D = S
---
-200p + 35,000 = -p^2 +400p - 20000
p^2 -600p +55000 = 0
---
I graphed it and found:
p = 112.92 or p = 487.08
================================
Cheers,
Stan H.