The revenue from selling x units of a product is given by y=-0.0002x^2+20x. How many must be sold in order to have the greatest revenue? Please show work.

The number of units that must be sold in order to have the greatest revenue is 50,000 units

Step-by-step explanation:

Given;

y = -0.0002x² + 20x

where;

y is the revenue

x is the units of the product

The equation above is a quadratic equation, to obtain the value of x (units) that will give maximum value of y (revenue), we differentiate the equation.

dy/dx = -0.0004x + 20

Now, equate the differential value to zero, in order to get the value of x that will make the equation maximum.

-0.0004x + 20 = 0

-0.0004x = -20

x = (-20) / (-0.0004)

x = 50,000 units

Therefore, the number of units that must be sold in order to have the greatest revenue is 50,000 units