Question 92912: 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.
sorry but I am so lost on this one, thank you
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! This problem came up a few days ago. I assume you are not the same person who submitted then. This is what I submitted then, hope it will help you.
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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.
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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 =< 40 - 2x
y =< (40/14) - (2/14)x
y =< 20/7 - (1/7)x; green line
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The production inequality:
x + y = 5
y = 5 - x; purple line
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Plot these two inequalities (I assume you know how to plot a graph, if not you
can email me at ankor@dixie-net.com and I will add the procedure to do that.)
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your graph should look like this:
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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
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