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.)
2007-05-28 15:46:11 · 4 answers · asked by JaNaLiEn 2 in Science & Mathematics ➔ Mathematics
Complete the square.
y = 0.0002 (x^2 + 100 000x)
= 0.0002 (x^2+ 100 000x + 2500000000) - 2500000000
= 0.0002 (x-50 000)^2 - 500 000
Therefore, 50 000 units must be sold.
2007-05-28 15:48:08 · answer #1 · answered by de4th 4 · 0⤊ 0⤋
Infinite amount of x's will give you the most. If you look at a graph of this, a is positive meaning you can only have a minimum value. You can also find the second derivative of this function to find out. A positive 2nd derivative will yield a minimum and a negative will yield a maximum. You can find the x coordinate by using -b/2a and find your y by plugging in the x value inside. There is another method to find y, but I find this helpful in research.
2007-05-28 22:53:09 · answer #2 · answered by UnknownD 6 · 0⤊ 0⤋
There is not enough information here--there needs to be a cost function to go along with this.
2007-05-28 22:50:21 · answer #3 · answered by bruinfan 7 · 0⤊ 0⤋
You must have stated the problem wrong. y is unbounded in this quadratic. In other words, there is no maximum profit.
2007-05-28 22:51:35 · answer #4 · answered by Anonymous · 0⤊ 0⤋