Question 76536: A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week. Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths. Then graph the system of inequalities.
Here is what i have so far:
x=40 items * 1 hour = 40 hours
y=20 items * 2 hours =40 hours
So I have the 60 items and the 80 hours, but how do I write a system of inequalities representing this and then how do I graph it. See I'm trying.
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! I was actually teaching this to a bunch of first year degree students, only a couple of weeks ago. If you're interested, this is how you begin a linear programming problem. Anyway. The first thing to do is identify our variables - this really only comes with practice, but normally you will find (at least in simple problems) the variables rae normally the things you can make.
In this case we have the number of bouquets (x) and the number of wreaths (y)
OK, the bouquests take 1 hour each to produce, and the wreaths take 2, so the amount of time to produce x bouquets and y wreats is  right? Now, labour is at a maximum of 80 hours so our first inequality is simply
The total production capacity is the amount of things we can make, yeah? so if we make x bouquets and y wreaths, then we make x+y things, agreed? We can make a maximum of 60 things so our next inequality is
WE must also never forget the non-negativity inequalities. Clearly we can't make -5 wreaths or -3 bouquets, so we also have
Now you have the inequalities, see if you can graph them. I think someone has written a lesson on here about graphing inequalities, so if you get stuck have a read of that. Or if that fails come back.
Hope that helps,
Kev
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