The total revenue for fred's Estates uc is given as the function $R(x)=400 x-0.5 x^{2}$, where $x$ is the number of apartinents filled. What number of apartments filied produces the maximum revenue?
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Final Answer: The number of apartments filled that produces the maximum revenue is \(\boxed{400}\).
Step 1 ：The total revenue for Fred's Estates UC is given by the function \(R(x)=400x-0.5x^{2}\), where \(x\) is the number of apartments filled.
Step 2 ：The revenue function is a quadratic function. The maximum value of a quadratic function \(ax^2 + bx + c\) is achieved at \(x = -\frac{b}{2a}\).
Step 3 ：In this case, \(a = -0.5\) and \(b = 400\).
Step 4 ：We need to calculate \(x = -\frac{400}{2*(-0.5)}\) to find the number of apartments that produces the maximum revenue.
Step 5 ：\(x = 400\)
Step 6 ：Final Answer: The number of apartments filled that produces the maximum revenue is \(\boxed{400}\).
