document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=342259>Question 342259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The relationship between the number of calculators x that<BR>\n" );
document.write( "a company can sell per month and the price of each calculator p is given by<BR>\n" );
document.write( "x = 1700 - 100p. Find the price at which a calculator should be sold to produce a<BR>\n" );
document.write( "monthly revenue of $7000. (Hint: Revenue = xp.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #245100 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=245100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1700+-100p ALIGN=MIDDLE  ALT=\"x+=+1700+-100p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7000+=+xp ALIGN=MIDDLE  ALT=\"7000+=+xp\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we have a system of two equations with two variables. Since the second equation is of degree 2 (because of the x*p term), we will use the Substitution Method. (With second degree equations other methods are often either not possible or not practical.)<br><BR>\n" );
document.write( "Since we already have the first equation solved for x, we will use that and substitute into the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7000+=+%281700-100p%29p ALIGN=MIDDLE  ALT=\"7000+=+%281700-100p%29p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To solve this we will start by simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7000+=+1700p-100p%5E2%29%7D%7D%0D%0ASince+this+is+a+quadratic+equation+we+want+one+side+to+be+zero%3A%0D%0A%7B%7B%7B100p%5E2+-1700p+%2B+7000+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can simplify the equation by dividing both sides by 100:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+-17p+%2B+70+=+0 ALIGN=MIDDLE  ALT=\"p%5E2+-17p+%2B+70+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can factor (or use the Quadratic Formula):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-7%29%28p-10%29+=+0 ALIGN=MIDDLE  ALT=\"%28p-7%29%28p-10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the Zero Product property we know that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-7+=+0 ALIGN=MIDDLE  ALT=\"p-7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-10+=+0 ALIGN=MIDDLE  ALT=\"p-10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving these we get:<BR>\n" );
document.write( "p = 7 or p = 10<BR>\n" );
document.write( "Now we find the x for each of these p's. We'll use the first equation and substitute in the value for p:<BR>\n" );
document.write( "For p = 7:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1700+-+100%287%29+=+1700+-+700+=+1000 ALIGN=MIDDLE  ALT=\"x+=+1700+-+100%287%29+=+1700+-+700+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For p = 10:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1700+-+100%2810%29+=+1700+-+1000+=+700 ALIGN=MIDDLE  ALT=\"x+=+1700+-+100%2810%29+=+1700+-+1000+=+700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So we have two solutions which generate $7000 revenue:<BR>\n" );
document.write( "When the price is $7, 1000 calculators will be sold.<BR>\n" );
document.write( "When the price is $10, 700 calculators will be sold.<br><BR>\n" );
document.write( "If it is cheaper to build 700 calculators than it would be to build 1000 calculators, the greatest profit would come from making 700 calculators and selling them for $10 each.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );