document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132198>Question 1132198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Johnson High school theater club is trying to set the price of tickets for a play.If the price is too low,they will not make enough money to cover expenses and if the price is too high,not enough people will pay the price of a ticket.They estimate that their total income per concert,I,in hundreds of dollars,can be approximated by the formula<BR>\n" );
document.write( "I=-x^2+24x-44,0 &#8804; x &#8804; 24 where x is the cost of a ticket<BR>\n" );
document.write( "a)draw the graph of income versus the cost of a ticket.<BR>\n" );
document.write( "b)Determine the minimum cost of a ticket for the theater club to break even.<BR>\n" );
document.write( "c)Determine the maximum cost of a ticket that the theater club can charge and break even.<BR>\n" );
document.write( "d)How much should they charge to receive maximum income?<BR>\n" );
document.write( "e)Find the maximum income.<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 #749151 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/123001.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "x represents the price of a ticket.<BR>\n" );
document.write( "y represents the income.\r<BR>\n" );
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document.write( "from the graph, it can be seen that:\r<BR>\n" );
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document.write( "when the cost of a ticket is 0 dollars, they will lose 44 dollars.<BR>\n" );
document.write( "when the cost of a ticket is 2 dollars, they will break even.<BR>\n" );
document.write( "when the cost of a ticket is 12 dollars, they will make 100 dollars.<BR>\n" );
document.write( "when the cost of a ticket is 22 dollars, they will break even.<BR>\n" );
document.write( "when the cost of a ticket is 24 dollars, they will lose 44 dollars.\r<BR>\n" );
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document.write( "answers to the questions are shown below:\r<BR>\n" );
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document.write( "a)draw the graph of income versus the cost of a ticket.<BR>\n" );
document.write( "done - see above.<BR>\n" );
document.write( "b)Determine the minimum cost of a ticket for the theater club to break even.<BR>\n" );
document.write( "2 dollars<BR>\n" );
document.write( "c)Determine the maximum cost of a ticket that the theater club can charge and break even.<BR>\n" );
document.write( "22 dollars<BR>\n" );
document.write( "d)How much should they charge to receive maximum income?<BR>\n" );
document.write( "12 dollars<BR>\n" );
document.write( "e)Find the maximum income.<BR>\n" );
document.write( "100 dollars\r<BR>\n" );
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document.write( "the break even income can also be found by factoring the quadratic equation.<BR>\n" );
document.write( "the maximum income can also be found by finding the value of x = -b/2a and then evaluating the equation with that value of x.\r<BR>\n" );
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document.write( "the equation is y = -x^2 + 24x - 44.<BR>\n" );
document.write( "to factor, do the following:<BR>\n" );
document.write( "set y equal to 0 to get -x^2 + 24x - 44 = 0<BR>\n" );
document.write( "multiply both sides by -1 to get (-1) * (x^2 - 24x + 44) = 0<BR>\n" );
document.write( "factor x^2 - 24x + 44 to get (x - 2) * (x - 22)<BR>\n" );
document.write( "the equation becomes (-1) * (x - 2) * (x - 22) = 0<BR>\n" );
document.write( "the equation will be equal to 0 when x = 2 or when x = 22 or when x = 2 and x = 22.\r<BR>\n" );
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document.write( "to find the maximum income, do the following:<BR>\n" );
document.write( "place the equation in standaed form of y = -x^2 + 24x - 44<BR>\n" );
document.write( "when in this form:<BR>\n" );
document.write( "a = coefficient of the x^2 term = -1<BR>\n" );
document.write( "b = coefficient of the x term = + 24<BR>\n" );
document.write( "c = constant term = -44<BR>\n" );
document.write( "the maximum income will be at x = -b/2a = -24/-2 = 12<BR>\n" );
document.write( "the maximum income will be -12^2 + 24*12 - 44 = 100\r<BR>\n" );
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document.write( "note that -12^2 is equal to - (12^2) and not equal to (-12)^2.<BR>\n" );
document.write( "the value that's being square is the 12, not the -12.\r<BR>\n" );
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document.write( "the graph confirms that the maximum value is at x = 12.<BR>\n" );
document.write( "the graph confirms that the income is 0 when x = 2 and when x = 22.<BR>\n" );
document.write( "the graph confirms that the school loses 44 dollars when x = 0 and when x = 24.\r<BR>\n" );
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