document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389446>Question 389446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carlos owns a vending machine in a bowling alley. He currently sells 600 cans of soda per week at $1.25 per can. He estimates that he will lose 40 customers for every increase in the price and gain 40 customers for every $0.05 decrease in the price. \r<BR>\n" );
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document.write( "1. Write a quadratic equation for the price increase<BR>\n" );
document.write( "2. If Carlos lowers the price, what price should he charge in order to maximize his income? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276011 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=276011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Carlos owns a vending machine in a bowling alley.<BR>\n" );
document.write( " He currently sells 600 cans of soda per week at $1.25 per can.<BR>\n" );
document.write( " He estimates that he will lose 40 customers for every increase in the price<BR>\n" );
document.write( " and gain 40 customers for every $0.05 decrease in the price.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1. Write a quadratic equation for the price increase<BR>\n" );
document.write( "Let x = no. of .05 increases<BR>\n" );
document.write( "Let x = no. of 40 customer decreases<BR>\n" );
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document.write( "f(x) = (1.25 + .05x)*(600 - 40x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "f(x) = 750 - 50x + 30x - 2x^2<BR>\n" );
document.write( "f(x) = -2x^2 - 20x + 750<BR>\n" );
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document.write( "2. If Carlos lowers the price, what price should he charge in order to maximize his income?<BR>\n" );
document.write( "Just change the signs of the above equation<BR>\n" );
document.write( "f(x) = (1.25 - .05x)*(600 + 40x)<BR>\n" );
document.write( "f(x) = 750 + 50x - 30x - 2x^2<BR>\n" );
document.write( "f(x) = -2x^2 + 20x + 750<BR>\n" );
document.write( "cost for max income will be at the axis of symmetry; x = -b/(2a)<BR>\n" );
document.write( "x = -2; b=20<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +5 ea .05 decreases in price, give 5(40) = 200 can increase<BR>\n" );
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document.write( "A .25 decrease; he should charge $1.00 for each soda, and will sell 800 cans<BR>\n" );
document.write( "a total: $800, which is $50 more than selling it at $1.25 (1.25*600=$750)<BR>\n" );
document.write( " </SPAN>\n" );
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