document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198187>Question 1198187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Basic calculus <BR>\n" );
document.write( "The selling price of a particular type of car is $20,000. The total cost of producing the car is TC = 2000 + X2.<BR>\n" );
document.write( "A.	Find the marginal revenue function?\r<BR>\n" );
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document.write( "B.	Find the marginal cost function? \r<BR>\n" );
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document.write( "C.	Find the quantity that maximizes profit?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848404 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **A. Find the Marginal Revenue Function**\r<BR>\n" );
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document.write( "* **Revenue (R):** <BR>\n" );
document.write( "    * Revenue is the selling price per unit multiplied by the number of units sold. <BR>\n" );
document.write( "    * R(X) = Selling Price * Quantity = $20,000 * X <BR>\n" );
document.write( "    * R(X) = $20,000X\r<BR>\n" );
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document.write( "* **Marginal Revenue (MR):** <BR>\n" );
document.write( "    * Marginal Revenue is the derivative of the revenue function with respect to the quantity. <BR>\n" );
document.write( "    * MR(X) = dR(X)/dX = d/dX ($20,000X) = $20,000\r<BR>\n" );
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document.write( "**B. Find the Marginal Cost Function**\r<BR>\n" );
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document.write( "* **Marginal Cost (MC):** <BR>\n" );
document.write( "    * Marginal Cost is the derivative of the total cost function with respect to the quantity.<BR>\n" );
document.write( "    * MC(X) = dTC(X)/dX = d/dX (2000 + X^2) = 2X\r<BR>\n" );
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document.write( "**C. Find the Quantity that Maximizes Profit**\r<BR>\n" );
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document.write( "* **Profit (P):** <BR>\n" );
document.write( "    * Profit is the difference between revenue and total cost.<BR>\n" );
document.write( "    * P(X) = R(X) - TC(X) = $20,000X - (2000 + X^2) <BR>\n" );
document.write( "    * P(X) = $20,000X - 2000 - X^2\r<BR>\n" );
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document.write( "* **To maximize profit, find the quantity (X) where the marginal revenue equals the marginal cost:** <BR>\n" );
document.write( "    * MR(X) = MC(X) <BR>\n" );
document.write( "    * $20,000 = 2X <BR>\n" );
document.write( "    * X = 10,000 \r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* The marginal revenue function is MR(X) = $20,000.<BR>\n" );
document.write( "* The marginal cost function is MC(X) = 2X.<BR>\n" );
document.write( "* The quantity that maximizes profit is 10,000 units.<BR>\n" );
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