linear equations

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lizzpalmer

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Each week at a furniture factory, 2000 work hours are available in the construction department, 1400 work hours in the painting department, and 1300 work hours in the packing department. Producing a chair requires 2 hours of construction, 1 hour of painting, and 2 hours for packing. Producing a table requires 4 hours of construction, 3 hours of painting, and 3 hours for packing. Producing a chest requires 8 hours of construction, 6 hours of painting, and 4 hours for packing. If all available time is used in every department, how many of each item is produced each week?

so, i know:

2x + 4y + 8z = 2000
1x + 3y + 6z = 1400
2x + 3y + 4z = 1300

but how do I solve the rest?

Thanks! This is due tomorrow - Sunday and I cant seem to get it!

Lizz
 
lizzpalmer said:
Each week at a furniture factory, 2000 work hours are available in the construction department, 1400 work hours in the painting department, and 1300 work hours in the packing department. Producing a chair requires 2 hours of construction, 1 hour of painting, and 2 hours for packing. Producing a table requires 4 hours of construction, 3 hours of painting, and 3 hours for packing. Producing a chest requires 8 hours of construction, 6 hours of painting, and 4 hours for packing. If all available time is used in every department, how many of each item is produced each week?

so, i know:

2x + 4y + 8z = 2000
1x + 3y + 6z = 1400
2x + 3y + 4z = 1300

but how do I solve the rest?

Thanks! This is due tomorrow - Sunday and I cant seem to get it!

Lizz
Click to expand...


I suggest you use CRAMER's rule which says find 3*3 matrix of coefficients and proceed finding 3*3 determinants where coeffs are substituted. Divide the deltax/delta

and do for x,y,z
 
burakaltr said:
I suggest you use CRAMER's rule which says find 3*3 matrix of coefficients and proceed finding 3*3 determinants where coeffs are substituted. Divide the deltax/delta

and do for x,y,z
Click to expand...

I think that answer is more advanced than I am lol.

I don't have a clue what that means.
 
lizzpalmer said:
I have to do it by hand without a calculator too to show my math.
Click to expand...

If you get to use Cramer you will find things are pretty easy

Let me try to explain :

Form determinant of coeffs, find delta

then for x, substitute the leftmost column by coeffs of x

Do for y ( middle column ),z (rightmost column )

then divide the latter found by deeterminant of coeffs to get x,y and z.
 
burakaltr said:
If you get to use Cramer you will find things are pretty easy

Let me try to explain :

Form determinant of coeffs, find delta

then for x, substitute the leftmost column by coeffs of x

Do for y ( middle column ),z (rightmost column )

then divide the latter found by deeterminant of coeffs to get x,y and z.
Click to expand...

I'm sorry, I don't understand.
 
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