The revenue from selling X units of a product is given by y=-0.0002x^2+20x. How many units must be sold in order to have the greatest revenue?(find the x-coordinate of the vertex of the parabola.)
2007-06-26 09:43:23 · 6 answers · asked by Berry A 2 in Science & Mathematics ➔ Mathematics
50,000 units
2007-06-26 09:54:09 · answer #1 · answered by God 3 · 0⤊ 0⤋
Just take the derivative of the function
d/dx(-.0002x^2+20x)
Which gives you this function
20-.0004x
Solve this to find the absolute max value
x =-20/-.0004
Which is x=50,000
Place this back in to the original equation if you want to find the y-value.
y=500,000
2007-06-26 17:01:41 · answer #2 · answered by crimsonedge 5 · 0⤊ 0⤋
You just want to find the maximum of the given function. Take its derivative and set it to zero. Its derivative is -0.0004x+20, so 0.0004x=20. So x=50,000.
2007-06-26 16:55:35 · answer #3 · answered by knivetsil 2 · 0⤊ 0⤋
remember the vertex is found by the formula x = -b / 2a
In this problem A = -0.0002 and b = 20
so x = -20 / 2(-0.0002) = 50,000 and since y is found by substituting 2 in for x
y = 0.0002(50,000)^2 + 20(50,000)
y = 1,500,000 so the point is (50,000 , 1,500,000)
2007-06-26 16:57:27 · answer #4 · answered by gfulton57 4 · 1⤊ 0⤋
y=0.0002x^2+20x
dy/dx=0.0004x+20=0,x=-20/0.0004=200000/4=50000.
d^2y/Dx^^2=0.0004=+
x=50000 gives minima of y.
2007-06-26 16:55:00 · answer #5 · answered by Anonymous · 0⤊ 1⤋
isn't it (20,0)?
its been summer for a long time where i live so i'm probably wrong.
2007-06-26 16:53:53 · answer #6 · answered by crayzperson01 1 · 0⤊ 0⤋