SOLUTION: 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

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Question 74648: 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.
Answer by stanbon(75887) About Me  (Show Source):
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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.
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Labor inequality:
2x+14y<=40
x+y<=5
0<=x<=5
0<=y<=5
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Solve each of the 1st two inequalities for "y":
y<=-(1/7)x+(20/7)
y<=-x+5
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Graph the Equalities and determine the
half-planes of the Inequalities:
graph%28400%2C300%2C-5%2C20%2C-5%2C20%2C%28-1%2F7%29x%2B%2820%2F7%29%2C-x%2B5%29
Cheers,
Stan H.