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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-> 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
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: =< +
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:
Area of feasibility would be at or below the lowest line (Positive values only)
:
Did this make sense to you? Any questions?
