QUESTION

Text
Image

# 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  