document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028198>Question 1028198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The relationship between the number of units sold of a certain product, x, and the price<BR>\n" );
document.write( "obtained, p, is:\r<BR>\n" );
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document.write( "x = 100-2p\r<BR>\n" );
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document.write( "a) Find an expression for the total revenue for selling x units of the product.\r<BR>\n" );
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document.write( "b) How many units must be sold for the marginal revenue to be 25?<BR>\n" );
document.write( "The total cost of producing x units of the product is:\r<BR>\n" );
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document.write( "TC (x)=0.5x^2+10x+100 \r<BR>\n" );
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document.write( "c) Find an expression for the profit when producing and selling x units of the product.\r<BR>\n" );
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document.write( "d) How many units must be produced and sold to obtain maximum profit?\r<BR>\n" );
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document.write( "e) What is 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 #644441 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 100 - 2p ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28100+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%28100+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a)  Revenue = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+xp+=+%28x%28100+-+x%29%29%2F2+=+-x%5E2%2F2+%2B50x ALIGN=MIDDLE  ALT=\"R%28x%29+=+xp+=+%28x%28100+-+x%29%29%2F2+=+-x%5E2%2F2+%2B50x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)  Marginal revenue is R'(x) = -x + 50.<BR>\n" );
document.write( "==> -x + 50 = 25 ==> -x = -25 ==> x = 25 units must be sold for the marginal revenue to be 25.\r<BR>\n" );
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document.write( "c)  Profit =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%28x%29+-+TC%28x%29+=+-x%5E2%2F2+%2B50x+-+x%5E2%2F2-10x+-+100+=+-x%5E2+%2B+40x+-100+ ALIGN=MIDDLE  ALT=\"+R%28x%29+-+TC%28x%29+=+-x%5E2%2F2+%2B50x+-+x%5E2%2F2-10x+-+100+=+-x%5E2+%2B+40x+-100+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "d)  Maximum number of units is obtained from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282a%29+=+-40%2F%282%2A-1%29+=+20 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282a%29+=+-40%2F%282%2A-1%29+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > units.\r<BR>\n" );
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document.write( "e)  maximum profit = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2820%29+=+-20%5E2+%2B40%2A20+-+100+=+-400+%2B800+-+100+=+300 ALIGN=MIDDLE  ALT=\"p%2820%29+=+-20%5E2+%2B40%2A20+-+100+=+-400+%2B800+-+100+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Thus the maximum profit is $300.\r<BR>\n" );
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