document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81512>Question 81512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small firm produces both AM and AM/FM car radios. The AM radios take 15 h<BR>\n" );
document.write( "to produce, and the AM/FM radios take 20 h. The number of production hours is<BR>\n" );
document.write( "limited to 300 h per week. The plant’s capacity is limited to a total of 18 radios per<BR>\n" );
document.write( "week, and existing orders require that at least 4 AM radios and at least 3 AM/FM<BR>\n" );
document.write( "radios be produced per week. Write a system of inequalities representing this situation.<BR>\n" );
document.write( "Then, draw a graph of the feasible region given these conditions, in which x<BR>\n" );
document.write( "is the number of AM radios and y the number of AM/FM radios. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58344 by </B><A HREF=/tutors/aboutme.mpl?userid=mathdoc316><B>mathdoc316(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathdoc316><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=58344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is how to do the word problem part:\r<BR>\n" );
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document.write( "First convert the english language in the problem to math language.\r<BR>\n" );
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document.write( "I will do this in two steps\r<BR>\n" );
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document.write( "The first step is to line up the facts individually like this\r<BR>\n" );
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document.write( "Time to produce one AM radio = 15<BR>\n" );
document.write( "Time to produce one AM/FM radio = 20<BR>\n" );
document.write( "Total production time <= 300<BR>\n" );
document.write( "Total radios produced <= 18<BR>\n" );
document.write( "Number of AM Radios produced >= 4<BR>\n" );
document.write( "Number of AM/FM Radios produced >= 3\r<BR>\n" );
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document.write( "The next step is to figure out the variables and constants.<BR>\n" );
document.write( "We want to rewrite all the constraints in algebraic terms.<BR>\n" );
document.write( "The problem states x is the number of AM radios and y is the number of AM/FM radios.<BR>\n" );
document.write( "The last two facts are:<BR>\n" );
document.write( "x >= 4<BR>\n" );
document.write( "y >= 3\r<BR>\n" );
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document.write( "Facts 1 and 2 can be used to translate facts 3 and 4 into math.\r<BR>\n" );
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document.write( "\"Total radios produced\" is x + y\r<BR>\n" );
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document.write( "Total production time is:<BR>\n" );
document.write( "  total time making AM radios<BR>\n" );
document.write( "  +<BR>\n" );
document.write( "  total time making AM/FM radios\r<BR>\n" );
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document.write( "Total time making AM radios is the number of AM radios multiplied by the amount of time needed to make an AM radio.  (Note: In a real factory, employees may not behave in a linear fashion.  However an assumption of linearity can be reasonable for a simple model.)\r<BR>\n" );
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document.write( "Total time making AM/FM radios is the number of AM/FM radios multiplied by the amount of time needed to make one AM/FM radio.\r<BR>\n" );
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document.write( "In math:<BR>\n" );
document.write( " Total production time: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+15%2Ax+%2B+20%2Ay ALIGN=MIDDLE  ALT=\"T+=+15%2Ax+%2B+20%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " Total radios:          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+x+%2B+y ALIGN=MIDDLE  ALT=\"R+=+x+%2B+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now all the constraints are:\r<BR>\n" );
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document.write( "  1. x >= 4<BR>\n" );
document.write( "  2. y >= 3<BR>\n" );
document.write( "  3. x + y <= 18<BR>\n" );
document.write( "  4. 15 x + 20 y <= 300\r<BR>\n" );
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document.write( "Also it is true that x and y are whole numbers.\r<BR>\n" );
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document.write( "Also we know x, y, T, and R are all >= 0 so you might want to<BR>\n" );
document.write( "graph that too.\r<BR>\n" );
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document.write( "I guess you already know how to graph - use the graphing tools on this site if it is a problem.  Or ask that part of the question again if that was the part you wanted help with.<BR>\n" );
document.write( "  <BR>\n" );
document.write( " </SPAN>\n" );
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