Find the number of units that produces maximum revenue given by
R = 900x-0.1x^2, where R is the total revenue in dollars and x is the number of units sold.
the roots of this equation are x=0, x=9000. The max will be half way between (its a parabola).
Now, as an intro to calculus, let me show something: The slope of R at the max is zero (it is a horizontal). Call Slope R' or dR/dx (rate of change of R with x).
R'=d/dx (900x-.1x^2)=0
or 900-.2x=0 or x=4500 at R max.
I want to know the answer pleasee
Ah, revenue maximization! It's like searching for the holy grail of business. Let's find that sweet spot!
So, we have the revenue equation R = 900x - 0.1x^2. To find the number of units that produces maximum revenue, we need to take the derivative of this equation with respect to x and set it equal to zero. Hang on, we're about to get mathematical!
Taking the derivative of R with respect to x, we get dR/dx = 900 - 0.2x. Setting this equal to zero, we have 900 - 0.2x = 0. Now, let's channel our inner mathematician and solve for x.
Subtracting 900 from both sides, we get -0.2x = -900. To get rid of that sneaky negative sign, we'll divide by -0.2. Mathematically speaking, x = -900 / -0.2. Tada! Simplifying it further, x = 4500.
So, the number of units that produces maximum revenue is 4500. Now go forth, sell those units, and make that revenue dance like nobody's watching!
To find the number of units that produce the maximum revenue, we need to find the derivative of the revenue function with respect to the number of units sold, set it equal to zero, and solve for x.
The total revenue function is given by R = 900x - 0.1x^2.
1. Take the derivative of the revenue function with respect to x:
dR/dx = 900 - 0.2x
2. Set the derivative equal to zero and solve for x:
900 - 0.2x = 0
Subtract 900 from both sides:
-0.2x = -900
Divide both sides by -0.2:
x = (-900) / (-0.2)
Simplify:
x = 4500
Therefore, the number of units that produces maximum revenue is 4500 units.