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# Your college newspaper, The Collegiate Investigator, sells for 90 per copy. The cost of producing $x$ copies of an edition is given by $C(x)=10+0.10 x+0.001 x^{2} \text { dollars. }$ (a) Calculate the marginal revenue $R^{\prime}(x)$ and profit $P^{\prime}(x)$ functions. HINT [See Example 2.] $\begin{array}{l} R^{\prime}(x)= \\ P^{\prime}(x)= \end{array}$ (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. \begin{tabular}{ll|l|l} revenue & $\$$& \\ profit & \$$ & \\ marginal revenue &$\$$& \\ marginal profit & \$$ & per additional copy \\ & & per additional copy \end{tabular} \begin{tabular}{ll|l|} revenue & $\$$& \\ profit & \$$ & \\ marginal revenue &$\$$& per additional copy \\ marginal profit & \$$ & per additional copy \end{tabular} Interpret the results. The approximate -- Select--- from the sale of the 501st copy is $\$$(c) For which value of$x$is the marginal profit zero?$x=$copies Interpret your answer. The graph of the profit function is a parabola with a vertex at$x=\$ , so the profit is at a maximum when you produce and sell copies. Need Help? Read It Talk to a Tutor  