document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181228>Question 1181228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each month ZV Corp (Zebra Vehicles where all paint jobs are striped) makes 230 A vehicles which get 10mpg,500 B vehicles which get 20mpg,and 70 C vehicles which get 40mpg.  Unfortunately, the government sets a standard where companies must “average”30mpg[this is called a CAFElaw].  Any company that falls short of the 30mpg standard must pay a penalty.  The penalty is calculated as $55times number of vehicles sold each month times the deficit in their average mpg from the 30mpg standard.\r<BR>\n" );
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document.write( "Compute ZV Corp’s monthly penalty if the government incorrectly uses (weighted) arithmetic mean to compute average mpg. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850068 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate ZV Corp's monthly penalty using the weighted arithmetic mean:\r<BR>\n" );
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document.write( "1. **Calculate the weighted average mpg:**\r<BR>\n" );
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document.write( "The weighted average mpg is calculated by multiplying each vehicle type's mpg by its proportion of total vehicles and then summing those results.\r<BR>\n" );
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document.write( "*   Total vehicles: 230 (A) + 500 (B) + 70 (C) = 800 vehicles\r<BR>\n" );
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document.write( "*   Weight of A vehicles: 230/800 = 0.2875<BR>\n" );
document.write( "*   Weight of B vehicles: 500/800 = 0.625<BR>\n" );
document.write( "*   Weight of C vehicles: 70/800 = 0.0875\r<BR>\n" );
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document.write( "Weighted average mpg = (0.2875 * 10) + (0.625 * 20) + (0.0875 * 40)<BR>\n" );
document.write( "Weighted average mpg = 2.875 + 12.5 + 3.5<BR>\n" );
document.write( "Weighted average mpg = 18.875 mpg\r<BR>\n" );
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document.write( "2. **Calculate the mpg deficit:**\r<BR>\n" );
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document.write( "Deficit = Standard mpg - Weighted average mpg<BR>\n" );
document.write( "Deficit = 30 mpg - 18.875 mpg<BR>\n" );
document.write( "Deficit = 11.125 mpg\r<BR>\n" );
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document.write( "3. **Calculate the total penalty:**\r<BR>\n" );
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document.write( "Penalty = $55 * Total vehicles * Deficit<BR>\n" );
document.write( "Penalty = $55 * 800 * 11.125<BR>\n" );
document.write( "Penalty = $489,500\r<BR>\n" );
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document.write( "Therefore, if the government incorrectly uses the weighted arithmetic mean, ZV Corp's monthly penalty would be $\boxed{489,500}$.<BR>\n" );
document.write( " </SPAN>\n" );
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