The revenue from selling x units of a product is given by y=-.0002x^2+20x How many units must be sold in order to have the greates revenue?
2006-11-03 06:54:22 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Take the derivative of the equation with regard to dx, and set it equal to zero. Then solve for x:
-.0004x + 20 = 0
.0004x = 20
x = 20/.0004 = 50,000 (QED)
2006-11-03 07:01:01 · answer #1 · answered by Dave 6 · 0⤊ 0⤋
The formula for the x coordinate of the vertex of a parabola is
x = -b / 2a where b = 20 and a = -.0002. Substituting, we get
the x value to be 50,000 units. If you want to get the max. revenue, substitute 50,000 units to the x in the revenue function and you will get 500,000 (dollars, if the unit of measure of revenue is in dollars)
2006-11-03 15:24:34 · answer #2 · answered by Ann R 2 · 0⤊ 0⤋
y=-.0002x^2+20x
y'=.004x+20
y"=.004>0
so there is no maximum, only a minimum at
0=.004x+20
x=-20/.004=-5000 which is physically impossible
in the range of 0<=x
there is no max.
2006-11-03 15:01:38 · answer #3 · answered by yupchagee 7 · 0⤊ 0⤋
The x coordinate of the vertex of a parabola is ( -b/2a )
-20/-.0002^2 (2) or -20/(2) .00000004=-20/.00000008= -250000000
2006-11-03 15:03:59 · answer #4 · answered by CV 1 · 0⤊ 0⤋
You just take derviative and set to 0.
SO, find x for -.0004x+20=0.
2006-11-03 15:00:06 · answer #5 · answered by yljacktt 5 · 0⤊ 0⤋