the revenue from selling x units of a product is given by y=-0.0002x^2+60x. how many units must be sold in order to have the greatest revenue?
I think I need to use this formula: -b/2a, but I'm not sure if I'm getting the right answer. please explain step by step.
thank you.
thanks again!
To find the point at which the revenue is maximized, you need to determine the x-value that corresponds to the maximum value of the revenue function. You are correct in thinking that the formula -b/2a can help you with this.
First, let's identify the coefficients in the revenue function:
a = -0.0002
b = 60
c = 0
Next, substitute the values of a and b into the formula -b/2a to find the x-value of the revenue function's maximum point:
x = -b / (2a)
x = -60 / (2 * (-0.0002))
x = -60 / (-0.0004)
x = 150,000
The x-value of 150,000 represents the number of units that must be sold in order to have the greatest revenue.
To understand why -b/2a works, consider that a quadratic function y = ax^2 + bx + c has a vertex at x = -b/2a. The vertex is the point where the function achieves its maximum (or minimum) value. In this case, the revenue function y = -0.0002x^2 + 60x is a downward-opening parabola because the coefficient of x^2 is negative. Therefore, the maximum revenue occurs at the vertex.
-b/2a is when x gives the maximum y.
-60/(2*-.0002)= you do it.