**QUESTION**

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Your college newspaper, The Collegiate Investigator, sells for $90 \notin$ 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.] \[ \begin{array}{l} R^{\prime}(x)=20 x \\ P^{\prime}(x)=\square \end{array} \] (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} revenue & $\$$ & \\ profit & $\$$ & per additional copy \\ marginal revenue & $\$$ & per additional copy \\ marginal profit & $\$$ & \end{tabular} \begin{tabular}{ll|l} revenue & $\$$ & \\ profit & $\$$ & per additional copy \\ marginal revenue & $\$$ & per additional copy \\ marginal profit & $\$$ & \end{tabular} Interpret the results. The approximate -- -Select--- 1 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.

Your monthly profit (in dollars) from selling magazines is given by \[ P=5 x+\sqrt{x} \] where $x$ is the number of magazines you sell in a month. If you are currently selling $x=50$ magazines per month, find your profit and your marginal profit. (Round your answers to two decimal places.) profit marginal profit $\$$ Interpret your answers. Your current profit is $\$$ per month, and would increase at a rate of \$ per additional magazine sold per month. Need Help? Read It Talk to a Tutor