Find the maximum revenue for the revenue function
R(x) = 352x − 0.6x2.
(Round your answer to the nearest cent.)
Don't forget your Algebra I now that you're taking precal
R(x) = x(352 - 0.6x)
The maximum occurs midway between the roots, at x = 293.33
So just find R(293.33) = 51626.67
Why did the revenue function go to the circus?
To find the maximum revenue, we need to determine the vertex of the parabolic equation. In this case, since the equation is in the form of R(x) = ax^2 + bx + c, the vertex can be found using the formula x = -b/2a.
So, for R(x) = 352x - 0.6x^2, a = -0.6 and b = 352.
Now, let's plug these values into the formula: x = -(352)/(2*(-0.6)).
After doing some math, x ≈ 293.33.
Now that we found the x-value of the vertex, we can plug it back into the revenue function to find the maximum revenue:
R(x) = 352x - 0.6x^2,
R(293.33) = 352(293.33) - 0.6(293.33)^2.
After crunching some numbers, the maximum revenue is approximately $51,930.67.
So, the maximum revenue for the revenue function R(x) = 352x - 0.6x^2 is approximately $51,930.67. Hope the funny math didn't make you laugh too much!
To find the maximum revenue, we need to find the vertex of the parabola formed by the revenue function R(x) = 352x - 0.6x^2.
The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, a = -0.6 and b = 352.
x = -352 / (2 * -0.6)
x = 352 / 1.2
x = 293.33 (rounded to two decimal places)
To find the maximum revenue, substitute the x value of the vertex into the revenue function:
R(293.33) = 352 * 293.33 - 0.6 * (293.33)^2
R(293.33) = 102933.32
Therefore, the maximum revenue is $102933.32, rounded to the nearest cent.
To find the maximum revenue, we need to find the vertex of the parabola represented by the revenue function R(x) = 352x - 0.6x^2.
The revenue function represents a downward-opening parabola since the coefficient of the x^2 term (-0.6) is negative. The vertex of a parabola given by the equation y = ax^2 + bx + c can be expressed as (-b/2a, f(-b/2a)), where f(x) is the function.
In this case, a = -0.6, b = 352, and c = 0. Thus, substituting these values into the formula for the x-coordinate of the vertex, we have:
x = -b / (2a)
= -352 / (2 * -0.6)
= -352 / -1.2
= 293.33 (rounded to two decimal places)
Now, to find the y-coordinate of the vertex, we substitute this value of x back into the function:
R(x) = 352x - 0.6x^2
R(293.33) ≈ 352(293.33) - 0.6(293.33^2)
≈ 103314.56
Therefore, the maximum revenue is approximately $103,314.56.