SOLUTION: hi i need help with this it is due tomm on mothers day and i cant figure it out. A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours

Question 81812: hi i need help with this it is due tomm on mothers day and i cant figure it out.
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 ankor@dixie-net.com(22740) (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.
:
x = no. of scarves; y = no. of sweaters:
:
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
:
The production inequality:
x + y = 5
y = 5 - x
:
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.)
:
your graph should look like this:

:
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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