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September 22nd, 2008, 06:57 PM   #1
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Gaus Elimination Help

Ok im totally stumped because the variables got switched up on me... here is the problem

A furniture copmany makes loungers, chairs, and footstools made out of wood, fabric and stuffing. The number of units of each of these materials needed for each of the products is given in the table below. How many of each product can be made if tehre are 54 units of wood, 63 units of fabric, and 43 units of stuffing availabe?

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September 22nd, 2008, 07:24 PM   #2
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Re: Gaus Elimination Help

Our unknowns are: how many of each type of chair can be made. So let # of loungers = l, # of chairs = c, and # of footstools = f.

Look at the amount of wood used first; there are 54 total units, and the table says how much each product uses:
54 = l+2c+3f

And the same with fabric:
63 = 2l+2c+f

and stuffing:
43 = 2l+c+f

Flipping the equations and putting them on top of each other gives:
l +2c+3f= 54
2l+2c+f = 63
2l +c+ f = 43

Does that help you set up the matrix? Or did you already get that far?
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September 23rd, 2008, 06:55 AM   #3
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Re: Gaus Elimination Help

You might look at it as you do in ratio and proportion. If the absolute amount of wood used in the loungers is "l", the amount of fabric and stuffing will be in the proportions 1:2:2. So the proportion in terms of absolute amounts will be l:2l:2l. This is stating that these are the absolute amounts of materials used in building the loungers. Let's follow along with this, using those absolute amounts:

loungers w:f:s = 1:2:2 = l:2l:2l
chairs w:f:s = 2:2:1 = 2c:2c:c
stuffing w:f:s = 3:1:1 = 3f:f:f

Now, looking down vertically, the total amount of wood used is l + 2c + 3f = 54
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September 23rd, 2008, 03:04 PM   #4
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Hi Kdocimo90, please explain what "the variables got switched up on me" means. Why were you stumped? Also, were you required to use Gaussian elimination to solve the problem?
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