document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66187>Question 66187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one less pumpkin for each 5 cent increase in price. What price should he charge to maximize his earnings?(Show algebraically)<BR>\n" );
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document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46922 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one less pumpkin for each 5 cent increase in price. What price should he charge to maximize his earnings?<BR>\n" );
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document.write( "Then amt sold will be (40-x); the price will be (1+.05x), y = total earnings<BR>\n" );
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document.write( "y = pumpkins sold * price:<BR>\n" );
document.write( "y = (40-x)(1+.05x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "y = 40 + 2x - 1x - .05x^2<BR>\n" );
document.write( "y = 40 + x - .05x^2<BR>\n" );
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document.write( "Put it in the standard y = ax^2 + bx + c form:<BR>\n" );
document.write( "y = -.05x^2 + x + 40<BR>\n" );
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document.write( "The max revenue(y) will occur at the vertex. Vertex equation: x = -b/(2a)<BR>\n" );
document.write( "In our equation a=-.05; b= 1<BR>\n" );
document.write( "x = -1/(2*-.05)<BR>\n" );
document.write( "x = -1/-.1<BR>\n" );
document.write( "x = 10 <BR>\n" );
document.write( "That means that the cost = $1 + (10*.05) = $1.50 a piece for max earnings<BR>\n" );
document.write( "Number of pumpkins sold will be 40 - 10 = 30 pumpkins sold at that price<BR>\n" );
document.write( "Total revenue: 30 * 1.50 = $45<BR>\n" );
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document.write( "A graphical presentation will make it clear to you:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+40%2C+-5%2C+50%2C+-.05x%5E2+%2B+x+%2B+40%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+40%2C+-5%2C+50%2C+-.05x%5E2+%2B+x+%2B+40%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the max earnings occurs when x = 10<BR>\n" );
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document.write( "He only needs to sell 30, that leaves 10 that he can give away or make pies or something, right? </SPAN>\n" );
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