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 82410: 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):
You can put this solution on YOUR website!
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,
Labor Inequality: 2x+14y<=40
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and the total production capacity is 5 items per week
Production Inequality:
0<=x<=5
0<=y<=5
x+y<=5
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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.
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Solve each inequality for y to get:
y <= (-1/7)x+(20/7)
y<=-x+5
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Then graph the system of inequalities
I can only graph the boundaries: You will have to determine
the respective half-plane solution areas:
graph%28400%2C300%2C-1%2C10%2C-1%2C10%2C%28-1%2F7%29x%2B%2820%2F7%29%2C-x%2B5%29
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Cheers,
Stan H.