Find the maximum revenue for the revenue function
R(x) = 383x − 0.6x2.
R(x) = 355x − 0.6x2.
Find the vertex of the parabola by first finding the x-value of the vertex by -b/2a
Then plug the x-value you got back into the original function R(x)
The y-value of the vertex is the max. revenue
To find the maximum revenue for the revenue function R(x) = 383x - 0.6x^2, we can use calculus.
Step 1: Take the derivative of the revenue function.
R'(x) = 383 - 1.2x
Step 2: Set the derivative equal to zero to find the critical point.
383 - 1.2x = 0
1.2x = 383
x = 383 / 1.2
x = 319.17 (rounded to two decimal places)
Step 3: Determine if the critical point is a maximum or minimum. To do this, we take the second derivative of the revenue function and evaluate it at the critical point.
R''(x) = -1.2
Since the second derivative is negative (-1.2), the critical point x = 319.17 is a maximum.
Step 4: Substitute the critical point back into the original revenue function to find the maximum revenue.
R(x) = 383x - 0.6x^2
R(319.17) = 383 * 319.17 - 0.6 * (319.17)^2
Calculating the above expression gives the maximum revenue.
To find the maximum revenue for the given revenue function R(x) = 383x - 0.6x^2, we need to determine the value of x that maximizes the function.
The maximum revenue occurs at the vertex of the parabolic function. The x-value of the vertex can be found using the formula:
x = -b / (2a)
In the given revenue function, a = -0.6 and b = 383. Substituting these values into the formula, we get:
x = -383 / (2*(-0.6))
Simplifying further:
x = -383 / (-1.2)
x = 319.17
Rounded to two decimal places, x ≈ 319.17.
To find the maximum revenue, substitute this value of x back into the original revenue function:
R(319.17) = 383(319.17) - 0.6(319.17)^2
Calculating this expression:
R(319.17) ≈ $61,269.23
Therefore, the maximum revenue for the given revenue function is approximately $61,269.23.