document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173668>Question 1173668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> QUADRATICS WORD PROBLEM<BR>\n" );
document.write( "An online, music service called peach music can sell 600 new subscription every week at $6.00per new subscription. The manager is considering increasing the price. A marketing survey showed that for every $0.50 increase in price, there would be 30 fewer new subscriptions.<BR>\n" );
document.write( "If x is the number of price increases and R is the revenue in dollars, this situation cann be moddle by the following equation: R=-15x^2+120x+3600<BR>\n" );
document.write( "a) What price should they set per subscription in order to obbtain the maximum weekly revenue?<BR>\n" );
document.write( "b)How many subsripton would they sell in order to achive this maximum revenue?<BR>\n" );
document.write( "Calculate the necessary values by first completing the square and then the quadratic formula. Show all your work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798939 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=798939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That is correct and comes from <BR>\n" );
document.write( "(600-30x)(6+0.5x)<BR>\n" );
document.write( "-<BR>\n" );
document.write( "-15x2+120x+3600=<BR>\n" );
document.write( "-(15x^2-120x) +3600)=<BR>\n" );
document.write( "-15(x^2-8x)+3600=<BR>\n" );
document.write( "-15(x^2-8x+16)+3600+240, to keep the equation in balance<BR>\n" );
document.write( "-15(x-4)^2+3840<BR>\n" );
document.write( "This quadratic is now in vertex form, and the vertex is (4, 3840).  That means the value of x maximizing the quadratic is 4 and f(x)=3840.\r<BR>\n" );
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document.write( "The quadratic formula will find the roots, which are -12 and 20, and the vertex is the axis of symmetry x value in between the roots or 4.\r<BR>\n" );
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document.write( "x=-(1/30) (-120+/- sqrt( 14400+216000)); sqrt (230400) is 480<BR>\n" );
document.write( "x=-12 and 20.\r<BR>\n" );
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document.write( "the price would be $8, and they would sell 480 subscriptions to make $3840.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Here is another way to check: <BR>\n" );
document.write( "the maximum is when x=-b/2a or -120/-30 or 4<BR>\n" );
document.write( "when x is 4<BR>\n" );
document.write( "that is 480 subscriptions at $8 for a maximum revenue of $3840.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-15%2C23%2C-250%2C4200%2C3840%2C-15x%5E2%2B120x%2B3600%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-15%2C23%2C-250%2C4200%2C3840%2C-15x%5E2%2B120x%2B3600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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