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 63440This question is from textbook
: 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. This question is from textbook

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, 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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1st: 2x+14y<=40
2nd: x+y<-5
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Solve 1st and 2nd for y and as an equality:
3rd: y<=(-2/14)x+(40/14)
y<=(-1/7)x+(20/7)
4th: y<=-x-5
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graph%28300%2C200%2C-20%2C10%2C-10%2C10%2C%28-1%2F7%29x%2B%2820%2F7%29%2C-x-5%29
Shade the half-plane below each line.
The union of each line with its half-plane is the graph you want.
Cheers,
Stan H.