Question 81595
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. 
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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. 
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x = no. of scarves; y = no. of sweaters:
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The labor inequality:
2x + 14y =< 40
Arrange in the general (y=) form so we can graph it:
14y =< - 2x + 40
y =< -(2/14)x + (40/14) 
y =< -(1/7)x + 20/7
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The production inequality:
x + y =< 5
y =< -x + 5
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Plot these two inequalities 
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your graph should look like this:
{{{ graph( 300, 200, -2, 8, -2, 8, -x+5, (1/7)x + (20/7)) }}}
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The area of feasibility would be at or below either line, whichever is lower
It's assumed that x and y => 0