Final answer:
To find the maximum revenue for the revenue function r(x) = 367x - 0.7x², we need to find the vertex of the function. By using the formula -b/2a, we can find the x-coordinate of the vertex. Substituting this value back into the revenue function, we can find the maximum revenue.
Step-by-step explanation:
To find the maximum revenue for the revenue function, we need to determine the maximum point of the function. This can be done by finding the vertex of the function. The formula for finding the x-coordinate of the vertex is -b/2a, where a, b, and c are the coefficients of the quadratic function in the form ax^2 + bx + c.
For the given function r(x) = 367x - 0.7x^2, a = -0.7 and b = 367. Plugging these values into the formula, we get:
x = -b/2a = -367/2(-0.7) = -367/(-1.4) = 262.14
The x-coordinate of the vertex is 262.14. To find the maximum revenue, we substitute this value back into the revenue function:
r(x) = 367(262.14) - 0.7(262.14)^2
r(x) = 96060.18
Therefore, the maximum revenue is $96060.18, rounded to the nearest cent, which is $96060.19.