SOLUTION: Hi I am trying to set up a problem involving the production of bouquets and wreaths. Bouquets take 1 hour and wreaths take 2 hours. Labor is limited to 80 hours per week and prod

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Question 111989: Hi I am trying to set up a problem involving the production of bouquets and wreaths. Bouquets take 1 hour and wreaths take 2 hours. Labor is limited to 80 hours per week and production capacity is limited to 60 items per week.
I know my first step is to write the two equations.
I am not certain if I write it like this as I also have to write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths and graph.
Let X = bouquets
Let y = wreaths
1x + 2y = 80 or would I use 60?
Then I have the other equation to write and I am not certain how to accomplish that.
This is a confusing problem and I would really like to know how to write the two equations correctly.
Thank you very much for your help.
Tracy


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
This same problem came up about a week ago. This is what I submitted then. Perhaps it will help you.
:
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.
:
Let x = no. of bouquets; y = no. of wreaths
:
Labor constraint:
1x + 2y =< 80
2y =< -x + 80
We want it to be 1y, so divide the equation by 2:
%282y%29%2F2 =< %28-x%29%2F2 + 80%2F2
y =< -.5x + 40; divided equation by 2 ( this is the form we want for graphing)
:
Production capacity constraint:
x + y =< 60
y =< -x + 60
:
Then graph the system of inequalities.
Plot two points for each:
y = -.5x + 40
x | y
-------
0 | 40: y = .5(0) + 40 = 40
50 | 15; y = .5(50) + 40 = 15
and
y = -x + 60
x | y
--------
0 | 60; y = 0 + 60 = 60
50 | 10; y = -50 + 60 = 10
:
Plot the above x/y coordinates and draw these two graphs, should look like this:
+graph%28+300%2C+200%2C+-10%2C+80%2C+-10%2C+80%2C+-.5x%2B40%2C+-x%2B60%29+
Area of feasibility would be at or below the lowest line (Positive values only)
:
Did this make sense to you? Any questions?