document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128496>Question 1128496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am beyond frustrated and failing to solve this, can anyone help please?\r<BR>\n" );
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document.write( "A company has determined that when x hundred dulcimers are&#8203; built, the average cost per dulcimer can be estimated by &#8203;C(x)=0.3x^2&#8722;2.7x+7.475&#8203;, where&#8203; C(x) is in hundreds of dollars. What is the minimum average cost per dulcimer and how many dulcimers should be built to achieve that&#8203; minimum?<BR>\n" );
document.write( "The minimum average cost per dulcimer is &#8203;$____.<BR>\n" );
document.write( "The company should build ____dulcimers to achieve the minimum.<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 #744965 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=744965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "For the general quadratic equation<BR>\n" );
document.write( "f(x) = ax^2 + bx + c<BR>\n" );
document.write( "the vertex point is (h,k) where h = -b/(2*a) and k = f(h)<BR>\n" );
document.write( "The min cost will occur at the vertex as the vertex is the lowest point when a > 0\r<BR>\n" );
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document.write( "Based on that general form above, we see that <BR>\n" );
document.write( "C(x) = 0.3x^2 - 2.7x + 7.475<BR>\n" );
document.write( "leads to these three coefficients:<BR>\n" );
document.write( "a = 0.3<BR>\n" );
document.write( "b = -2.7<BR>\n" );
document.write( "c = 7.475\r<BR>\n" );
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document.write( "Plug in the values of 'a' and 'b' to find h<BR>\n" );
document.write( "h = -b/(2*a)<BR>\n" );
document.write( "h = -(-2.7)/(2*0.3)<BR>\n" );
document.write( "h = 2.7/0.6<BR>\n" );
document.write( "h = 4.5<BR>\n" );
document.write( "This is the x coordinate of the vertex\r<BR>\n" );
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document.write( "Now plug in x = 4.5 to find the value of k<BR>\n" );
document.write( "C(x) = 0.3x^2 - 2.7x + 7.475<BR>\n" );
document.write( "C(4.5) = 0.3(4.5)^2 - 2.7(4.5) + 7.475<BR>\n" );
document.write( "C(4.5) = 0.3(20.25) - 2.7(4.5) + 7.475<BR>\n" );
document.write( "C(4.5) = 6.075 - 12.15 + 7.475<BR>\n" );
document.write( "C(4.5) = 1.4<BR>\n" );
document.write( "k = C(h) = C(4.5) = 1.4\r<BR>\n" );
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document.write( "Therefore, the vertex point is (h,k) = (4.5, 1.4)\r<BR>\n" );
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document.write( "The minimum average cost per dulcimer is $__<u><font size=4 color=red>1.40</font></u>__.<BR>\n" );
document.write( "The company should build __<u><font size=4 color=red>450</font></u>__dulcimers to achieve the minimum.\r<BR>\n" );
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document.write( "note: x is the number of dulcimers built and this number is in hundreds. So x = 4.5 indicates 4.5 hundred or 4.5*100 = 450 units are built.<BR>\n" );
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