SOLUTION: suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars, the revenue r (in dollars) as a function of the price p is r(p)=-2.5p^2+550p. (a) fo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars, the revenue r (in dollars) as a function of the price p is r(p)=-2.5p^2+550p. (a) fo      Log On


   

Question 927621: suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars, the revenue r (in dollars) as a function of the price p is r(p)=-2.5p^2+550p. (a) for what price will the revenue be maximized? (b) what is the maximum revenue?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the form of the equation is
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+, the
value of +x+ where f(x) is a maximum
occurs at +-b%2F%282a%29+
------------------------
+r%28p%29+=+-2.5p%5E2+%2B+550p+
+p%5Bmax%5D+=+-550%2F%28-2.5%2A2%29+
+p%5Bmax%5D+=+550%2F5+
+p%5Bmax%5D+=+110+
(a)
At a price of $110 the revenue is maximized
-----------------
(b)
+r%28p%29+=+-2.5p%5E2+%2B+550p+
+r%5Bmax%5D+=+-2.5%2A110%5E2+%2B+550%2A110+
+r%5Bmax%5D+=+-30250+%2B+60500+
+r%5Bmax%5D+=+30250+
The maximum revenue is $30,250
--------------------------------
Here's a plot:
+graph%28+400%2C+400%2C+-50%2C+250%2C+-10000%2C+35000%2C+-2.5x%5E2+%2B+550x+%29+