document.write( "Question 51388: I am no good with word problems, please help!\r
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\n" ); document.write( "\n" ); document.write( "A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to produce, and the AM/FM radios take 20 h. The number of production hours is limited to 300 h per week. The plant's capacity is limited to a total of 18 radios per week, and exisitng orders require that at least 4 AM radios and at least 3 AM/FM radios be produced per week. Write a system of inequalities representing this situation. Then draw a graph of the feasible region given these conditions, in which x is the number of AM radios and y the number of AM/FM radios. \n" ); document.write( "
Algebra.Com's Answer #34335 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to\r\n" );
document.write( "produce, and the AM/FM radios take 20 h. The number of production hours is\r\n" );
document.write( "limited to 300 h per week. The plant's capacity is limited to a total of 18\r\n" );
document.write( "radios per week, and exisitng orders require that at least 4 AM radios and at\r\n" );
document.write( "least 3 AM/FM radios be produced per week. Write a system of inequalities\r\n" );
document.write( "representing this situation. Then draw a graph of the feasible region given\r\n" );
document.write( "these conditions, in which x is the number of AM radios and y the number of\r\n" );
document.write( "AM/FM radios.\r\n" );
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document.write( ">>>...require that at least 4 AM radios...be produced per week...<<<\r\n" );
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document.write( "Translation: x is greater than or equal to 4\r\n" );
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document.write( "            x > 4\r\n" );
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document.write( ">>>...require that...at least 3 AM/FM radios be produced per week...<<<\r\n" );
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document.write( "Translation: y is greater than or equal to 3\r\n" );
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document.write( "            y > 3\r\n" );
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document.write( ">>>...The plant's capacity is limited to a total of 18 radios per week...<<\r\n" );
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document.write( "Translation: x and y added together can't be more than 18\r\n" );
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document.write( "        x + y > 18\r\n" );
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document.write( ">>>...The AM radios take 15 h [each] to produce...<<\r\n" );
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document.write( "Translation: to produce x AM radios takes 15x hours\r\n" );
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document.write( ">>>...the AM/FM radios take 20 h [each]...<<<\r\n" );
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document.write( "Translation: to produce y AM/FM radios takes 20y hours.\r\n" );
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document.write( ">>>...The number of production hours is limited to 300 h per week...<<\r\n" );
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document.write( "Translation: 15x hours and 20y hours together must be less than or\r\n" );
document.write( "             equal to 300 hours\r\n" );
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document.write( "             15x + 20y < 300\r\n" );
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document.write( "We have this system of inequalities:\r\n" );
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document.write( "                     x > 4\r\n" );
document.write( "                     y > 3\r\n" );
document.write( "                 x + y > 18\r\n" );
document.write( "             15x + 20y < 300\r\n" );
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document.write( "We now graph the four boundary lines whose equations are the\r\n" );
document.write( "above inequalities with equal signs replacing to inequality\r\n" );
document.write( "signs.\r\n" );
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document.write( "                     x = 4\r\n" );
document.write( "                     y = 3\r\n" );
document.write( "                 x + y = 18\r\n" );
document.write( "             15x + 20y = 300\r\n" );
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document.write( "x = 4 is a vertical line 4 units right of the y-axis\r\n" );
document.write( "y = 3 is a horixontal line 3 units above the x-axis\r\n" );
document.write( "x + y = 18 has intercepts (18, 0) and (0, 18)\r\n" );
document.write( "15x + 20y = 300 has intercepts (20, 0) and (0, 15)\r\n" );
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document.write( "Draw the 4 lines\r\n" );
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document.write( "The feasible region is supposed to be shaded.  I can't do that on here,\r\n" );
document.write( "but it's the region which is to the right of the vertical line, above\r\n" );
document.write( "the horizontal line and below both slanted lines.\r\n" );
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document.write( "Edwin

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