SOLUTION: The owner of a small clothing company wants to create a mathematical model for the company�s daily profit, p, in dollars, based on the selling price, d, in dollars, of the dresses

Question 1080606: The owner of a small clothing company wants to create a mathematical model for the company�s daily profit, p, in dollars, based on the selling price, d, in dollars, of the dresses made. The owner has noticed that the maximum daily profit the company has made is $2300. This occurred when the dresses were sold for $110 each. The owner also noticed that selling the dresses for $90 resulted in a profit of $1600. Using a quadratic relation to model this problem, create an equation for the company�s daily profit.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Plot profit, on the vertical axis and
selling price of a dress, on the horizontal axis
-------------------------------------------------
If the relation is quadratic, then the equation
must look like:

----------------------------
You are given 2 points:
( 110, 2300 ) ( the maximum )
( 90, 1600 )
-----------------------------------
For the maximum,

(1)
and

(2)
--------------------------------------
( 90, 1600 )

(3)
--------------------------------------
Subtract (3) from (2)
(2)
(3)
--------------------------------------

Plug (1) into this result

and
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
----------------------------
The equation is:

-----------------------------------
check:

( as it should be )
--------------------------------------
Plug this result into equation

( as it should be )
You can check the other point, ( 90, 1600 )

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