document.write( "Question 126198: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities. \n" ); document.write( "
Algebra.Com's Answer #92546 by ankor@dixie-net.com(22740)\"\" \"About 
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A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities.
\n" ); document.write( ":
\n" ); document.write( "x = no. of scarves; y = no. of sweaters:
\n" ); document.write( ":
\n" ); document.write( "The labor (in hours) inequality:
\n" ); document.write( "2x + 14y =< 40
\n" ); document.write( "Arrange in the general (y=) form so we can graph it:
\n" ); document.write( "14y =< -2x + 40
\n" ); document.write( "y =< -(2/14)x + (40/14)
\n" ); document.write( "y =< -(1/7)x + 20/7
\n" ); document.write( ":
\n" ); document.write( "Plot this equation:
\n" ); document.write( "For x = 0
\n" ); document.write( "y = -(1/7)(0) + 20/7
\n" ); document.write( "y = 20/7 or about 2.85
\n" ); document.write( ":
\n" ); document.write( "For x = 7
\n" ); document.write( "y = -(1/7)(7) + (20/7)
\n" ); document.write( "y = -1 + 20/7
\n" ); document.write( "y = -(7/7) + (20/7)
\n" ); document.write( "y = +13/7 or about 1.85
\n" ); document.write( ":
\n" ); document.write( "A table of the x/y coordinates:
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( " 0 | 2.85
\n" ); document.write( " 7 | 1.85
\n" ); document.write( "Join these two points with a straight-edge for the labor graph
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "The production inequality:
\n" ); document.write( "x + y = 5
\n" ); document.write( "y = 5 - x
\n" ); document.write( ":
\n" ); document.write( "Plot this equation:
\n" ); document.write( "For x = 0, then y = 5, obviously
\n" ); document.write( ":
\n" ); document.write( "For x = 4
\n" ); document.write( "y = 5 - 4
\n" ); document.write( "y = 1
\n" ); document.write( ":
\n" ); document.write( "The table for these x/y coordinates
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( " 0 | 5
\n" ); document.write( " 4 | 1
\n" ); document.write( "Join these to points for the production graph
\n" ); document.write( ":
\n" ); document.write( "your graph should look like this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+8%2C+-2%2C+8%2C+5-x%2C+%2820%2F7%29+-+%281%2F7%29x%29+\"
\n" ); document.write( ":
\n" ); document.write( "The area of feasibility would be at or below either line, whichever is lower
\n" ); document.write( "It's assumed that x and y => 0
\n" ); document.write( ":
\n" ); document.write( "It looks like the best you could do is 3 scarfs and 2 sweaters
\n" ); document.write( ":
\n" ); document.write( "Did this help?
\n" ); document.write( " \n" ); document.write( "
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