Choose the one alternative that best completes the statement or answers the question.
-Economists use what is called a Leffer curve to predict the government revenue for tax rates from $0 \%$ to $100 \%$. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces t maximum revenue. Suppose an economist produces this rational function
$R ( x ) = \frac { 10 x ( 100 - x ) } { 75 + x }$, where $R$ is revenue in millions at a tax rate of $x$ percent. Use a graphing calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue?
A) $37.5 \% ; \$ 210$ million
B) $39.6 \% ; \$ 209$ million
C) $34.9 \% ; \$ 207$ million
D) $35.8 \% ; \$ 209$ million

Question

Quizplus · Accepted Answer

To find the tax rate that produces the maximum revenue and the maximum revenue itself, one would typically use calculus or a graphing calculator to analyze the function $R(x) = \frac{10x(100-x)}{75+x}$. However, without performing the calculations directly here, the correct answer is based on the premise of the question. The maximum revenue and corresponding tax rate can be determined by graphing the function and finding the vertex of the curve or by using optimization techniques. Among the given options, $39.6\%$ tax rate producing \$209 million in revenue is identified as the correct choice based on the context provided.

Choose the One Alternative That Best Completes the Statement or Answers