Find the maximum revenue for the revenue function
R(x) = 359x − 0.6x2.
(Round your answer to the nearest cent.)
R = $
the max is on the axis of symmetry of the graph
x = -b / (2 a) = -359 / (2 * -0.6)
find x
plug into R(x) to find max revenue
To find the maximum revenue for the given revenue function R(x) = 359x - 0.6x^2, you need to find the maximum value of R(x). This can be done by finding the vertex of the quadratic equation.
The general form of a quadratic equation is ax^2 + bx + c, where "a" is the coefficient of x^2, "b" is the coefficient of x, and "c" is the constant term.
In this case, the equation is R(x) = -0.6x^2 + 359x. Comparing it to the general form, we have:
a = -0.6
b = 359
c = 0 (since there is no constant term)
The x-coordinate of the vertex of a quadratic equation can be found using the formula: x = -b / (2a).
Substituting the values, we have:
x = -359 / (2(-0.6))
x = -359 / (-1.2)
x = 299.17 (rounded to the nearest cent)
Now, substitute this value back into the original equation to find the maximum revenue:
R(x) = -0.6(299.17)^2 + 359(299.17)
R(x) = -53994.22 + 107921.03
R(x) = 53926.81 (rounded to the nearest cent)
Therefore, the maximum revenue for the given function is $53,926.81.