document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198755>Question 1198755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the demand equation for a monopolist’s product is  P=400-2Q and the average cost function is AC=400/Q+4+0.2Q , where Q is the number of units and p is the price per unit.<BR>\n" );
document.write( "	Write down the equations for TC and TR. <BR>\n" );
document.write( "Calculate the price and quantity at which profit is maximised. Determine the maximum 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 #848286 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Total Cost (TC) Equation**\r<BR>\n" );
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document.write( "* **Total Cost (TC) = Average Cost (AC) * Quantity (Q)**<BR>\n" );
document.write( "* TC = (400/Q + 4 + 0.2Q) * Q<BR>\n" );
document.write( "* TC = 400 + 4Q + 0.2Q²\r<BR>\n" );
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document.write( "**2. Find the Total Revenue (TR) Equation**\r<BR>\n" );
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document.write( "* **Total Revenue (TR) = Price (P) * Quantity (Q)**<BR>\n" );
document.write( "* TR = (400 - 2Q) * Q<BR>\n" );
document.write( "* TR = 400Q - 2Q²\r<BR>\n" );
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document.write( "**3. Find the Profit (π) Equation**\r<BR>\n" );
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document.write( "* **Profit (π) = Total Revenue (TR) - Total Cost (TC)**<BR>\n" );
document.write( "* π = (400Q - 2Q²) - (400 + 4Q + 0.2Q²)<BR>\n" );
document.write( "* π = 400Q - 2Q² - 400 - 4Q - 0.2Q²<BR>\n" );
document.write( "* π = 396Q - 2.2Q² - 400\r<BR>\n" );
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document.write( "**4. Find the Quantity that Maximizes Profit**\r<BR>\n" );
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document.write( "* To find the quantity that maximizes profit, we need to find the derivative of the profit function with respect to Q and set it to zero.<BR>\n" );
document.write( "* dπ/dQ = 396 - 4.4Q = 0<BR>\n" );
document.write( "* 4.4Q = 396<BR>\n" );
document.write( "* Q = 90\r<BR>\n" );
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document.write( "**5. Find the Price at Maximum Profit**\r<BR>\n" );
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document.write( "* Substitute the optimal quantity (Q = 90) into the demand equation:<BR>\n" );
document.write( "* P = 400 - 2 * 90<BR>\n" );
document.write( "* P = 400 - 180<BR>\n" );
document.write( "* P = $220\r<BR>\n" );
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document.write( "**6. Calculate the Maximum Profit**\r<BR>\n" );
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document.write( "* Substitute the optimal quantity (Q = 90) into the profit function:<BR>\n" );
document.write( "* π = 396 * 90 - 2.2 * 90² - 400<BR>\n" );
document.write( "* π = 35640 - 17820 - 400<BR>\n" );
document.write( "* π = $17420\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **Quantity that maximizes profit:** 90 units<BR>\n" );
document.write( "* **Optimal price:** $220<BR>\n" );
document.write( "* **Maximum profit:** $17,420<BR>\n" );
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