Question 970677: 34 four workers are available to assemble tables and chairs. it takes 5 people to assemble a table and 3 people to assemble a chair. the workers always at least 4 chairs for every one table what is the maximum total number of chairs and tables that can be made?
Find the constraints, equation to optimize and the maximum.
so I tried this problem and I was told I did it wrong I said that x is tables and y is chairs. so x should be more than or equal to zero as well as y.
I don't know the other constraints.
it's an optimization problem. the thing I struggle with most is the constraints and the equation to optimize.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 34 workers are available to assemble tables and chairs.
Note: That is a constraint
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it takes 5 people to assemble a table and 3 people to assemble a chair. the
That gives you the following people Inequality::
5t + 3c <= 34 people
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workers always make at least 4 chairs for every one table
That is a constraint:: c >= 4t
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what is the maximum total number of chairs and tables that can be made?
Find the constraints, equation to optimize and the maximum.
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Rearrange the 2 inequlities so you can graph them::
You graph in the 1st quadrant because c >= 0 and t is >= 0
c >= 4t
c <=(-5/3)t + (34/3)
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Find the intersection of the borders:
Solve:
4t = (5/3)t + (34/3)
(7/3)t = (34/3)
7t = 34
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Comment:: I'm beginning to think the number of workers is 35, not 34.
If it is 35 you get:
t = 5 and c = 20 as one of the vertices
The other vertices are (0,0) and (0,35/3)
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Ans: Choose the vertex that gives you the maximum
number of tables and chairs.
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Hope this helps.
Cheers,
Stan H.
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