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 73080This question is from textbook Beginning Algebra
: 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 Beginning Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
:
x = number of scarves, y = number of sweaters
;
The labor constraint:
2x + 14y =< 40
Put in the general "y=" form in order to graph it
14y =< 40 - 2x
y =< (40/14) - (2/14)x
y =< (20/7) - (1/7)x
;
The production constraint
x + y =< 5
y =< 5 - x
:
the graph:
+graph%28+300%2C+200%2C+-2%2C+6%2C+-2%2C+6%2C+%2820%2F7%29-%281%2F7%29x%2C+5-x%29+
:
Area of feasibility is at or below both lines, whichever is lower.