document.write( "Question 23045: You plan to put a fence around a rectangular lot. The length of the lot must be at least 70ft. The cost for the fence along the length of the lot is $2 per foot, and the cost of the fence along the width is $3 per foot. The total cost can not exceed $360.\r
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Algebra.Com's Answer #11597 by AnlytcPhil(1806)\"\" \"About 
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You plan to put a fence around a rectangular lot. The length of the lot must be\r\n" );
document.write( "at least 70ft. The cost for the fence along the length of the lot is $2 per\r\n" );
document.write( "foot, and the cost of the fence along the width is $3 per foot. The total cost\r\n" );
document.write( "can not exceed $360. \r\n" );
document.write( "a. Use two variables to write a system of inequalities that models the problem\r\n" );
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document.write( "Let x = the length and y = the width\r\n" );
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document.write( " ___________\r\n" );
document.write( "|     x     | \r\n" );
document.write( "|           |y\r\n" );
document.write( "|           |\r\n" );
document.write( "|___________|\r\n" );
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document.write( ">>...The length of the lot must be at least 70ft...<<\r\n" );
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document.write( "Translation:  x >= 70\r\n" );
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document.write( ">>...The cost for the fence along the length of the lot is $2 per foot,...<<\r\n" );
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document.write( "Translation: cost along the two lengths is $2 times 2x (there are two\r\n" );
document.write( "lengths). This amounts to 2(2x) or 4x.\r\n" );
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document.write( ">>...the cost of the fence along the width is $3 per foot...<<\r\n" );
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document.write( "Translation: cost along the two widths is $3 times 2y (there are two\r\n" );
document.write( "widths). This amounts to 3(2y) or 6y.\r\n" );
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document.write( ">>...The total cost can not exceed $360...<<\r\n" );
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document.write( "Translation 4x + 6y <= 360\r\n" );
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document.write( "We must also require that the variables x and y are not negative. x >= 70\r\n" );
document.write( "meets this requirement, so we only need y >= 0\r\n" );
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document.write( "x >= 70\r\n" );
document.write( "4x + 6y <= 360 \r\n" );
document.write( "y >= 0\r\n" );
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document.write( "These are the inequalities which model the problem.\r\n" );
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document.write( "b. Graph the system, and shade the feasible region.\r\n" );
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document.write( "Draw the graphs of the boundary lines\r\n" );
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document.write( "x = 70           a vertical line through (70,0)\r\n" );
document.write( "4x + 6y = 360    a slanted line from (0,60) to (90,0)\r\n" );
document.write( "y = 0            the x-axis\r\n" );
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document.write( "The feasible region is a triangle whose corners are\r\n" );
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document.write( "(70, 0), (70, 13 1/3) and (90,0)\r\n" );
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document.write( "Shade this triangle. \r\n" );
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document.write( "----------------------------------------------------------------\r\n" );
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document.write( "c.What is the maximum width of the lot if the length is 60 feet?\r\n" );
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document.write( "y is the width and the maximum value must occur at one of the corner\r\n" );
document.write( "points.  Thus the maximum value of y is at the corner point (70, 13 1/3),\r\n" );
document.write( "so the maximum width is 13 1/3 feet.  (A very narrow lot, really a strip)\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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