document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965267>Question 965267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Must develop a quadratic function in order to solve the problem: A store sells 6000 gallons of paint each week for $15 per gallon. For each $1 decrease in the price, the store will sell an additional 1000 gallons each week. What should the sale price be to maximize the income?\r<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 #590004 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=590004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PRICE*UNITSSOLD=REVENUE\r<BR>\n" );
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document.write( "15*6000=R<BR>\n" );
document.write( "(15-1)*(6000+1000)=R(1)<BR>\n" );
document.write( "(15-2)(6000+2*1000)=R(2)<BR>\n" );
document.write( "(15-3)(6000+3*1000)=R(3)<BR>\n" );
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document.write( "The variable here is the amount of decrease from the initial 15 dollar per gallon price, so the variable choice this way can be x, the amount of price DECREASED off the $15.\r<BR>\n" );
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document.write( "Formula for revenue is the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=%2815-x%29%286000%2B1000x%29 ALIGN=MIDDLE  ALT=\"R%28x%29=%2815-x%29%286000%2B1000x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Do the simplifying into general form, and you'll have the quadratic equation to which you can apply the general solution for a quadratic equation; but what you want is the value for x in the MIDDLE of the zeros of R.  That will be the maximum, because R(x) is a function with a maximum point  (according to the coefficient on x^2 being negative).\r<BR>\n" );
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document.write( "If that analysis makes sense, after you read and think about it carefully, then you know what to do.  Just remember, as analyzed here, the price you are looking for is 15 MINUS the middle value between the zeros.\r<BR>\n" );
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document.write( "Note, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=1000%2815-x%29%286%2Bx%29 ALIGN=MIDDLE  ALT=\"R%28x%29=1000%2815-x%29%286%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so when you examine the roots, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=1000%2815-x%29%28x%2B6%29 ALIGN=MIDDLE  ALT=\"0=1000%2815-x%29%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by 1000,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%2815-x%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%2815-x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "...and again, look for the x value exactly between the two zeros. </SPAN>\n" );
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