# Thread: System of Equations with 2 and 3 Variables

1. ## System of Equations with 2 and 3 Variables

Hello,

First of all I want to apologize if did not post in the right place.
I need your help to find the right tool for solving practical problem.

My data includes information for number of Items produced for a day and total time for the production. The problem is that one employee can produce 3 different kinds of items with different level of difficulty.
My goal is to measure average time for the 3 items based on the information for total time and number for each item.
My idea was to make a system of equation from each two days in which the employee has values for two of the items and another system for the days in which there is values for the 3 items. Then, using the results for x,y and z from each system to find the average value for x,y and z.
50x + 30y = 450 min
45x + 15y = 400 min

45x + 1y + 14z = 420
33x + 20y + 15z = 450
50x + 15y + 10z = 400

etc............

If values for example are: x =7 y= 9 z = 10 then i am finding the weight of y and z like this:
7 9 10
x y z
1 9/7=1.285 1.428

From here I can transfer items B and C to items A
If:
ItemA ItemB ItemC
1000 600 400
Then
1000 ItemA + 600*1.285 + 400*1.482 = Total Production Time

The problem here is that the time for each of the items can vary for each day in a way that I am getting negative numbers in the results of the system.

So now when you know what I am trying to do can you please tell me how can I obtain the most reliable results for x, y and z?

Many thanks for the help!

2. Originally Posted by ndb
Hello,

First of all I want to apologize if did not post in the right place.
I need your help to find the right tool for solving practical problem.

My data includes information for number of Items produced for a day and total time for the production. The problem is that one employee can produce 3 different kinds of items with different level of difficulty.
My goal is to measure average time for the 3 items based on the information for total time and number for each item.
My idea was to make a system of equation from each two days in which the employee has values for two of the items and another system for the days in which there is values for the 3 items. Then, using the results for x,y and z from each system to find the average value for x,y and z.
50x + 30y = 450 min
45x + 15y = 400 min

45x + 1y + 14z = 420
33x + 20y + 15z = 450
50x + 15y + 10z = 400

etc............

If values for example are: x =7 y= 9 z = 10 then i am finding the weight of y and z like this:
7 9 10
x y z
1 9/7=1.285 1.428

From here I can transfer items B and C to items A
If:
ItemA ItemB ItemC
1000 600 400
Then
1000 ItemA + 600*1.285 + 400*1.482 = Total Production Time

The problem here is that the time for each of the items can vary for each day in a way that I am getting negative numbers in the results of the system.

So now when you know what I am trying to do can you please tell me how can I obtain the most reliable results for x, y and z?

Many thanks for the help!
$\displaystyle \begin{bmatrix} 50 & 30 & :450\\ 45 & 15 & :400 \end{bmatrix}$ Then do rref to solve for x and y. Set up the same matrix for the next problem

3. Well that is what I have been doing, but in some cases I am getting negative numbers in the result. What should I do so to obtain only positive numbers??

4. Originally Posted by ndb
Well that is what I have been doing, but in some cases I am getting negative numbers in the result. What should I do so to obtain only positive numbers??

If you do the rref correctly, you won't obtain negative values.

50x + 30y = 450 min
45x + 15y = 400 min

45x + 1y + 14z = 420
33x + 20y + 15z = 450
50x + 15y + 10z = 400

What the results should be? I am not sure I can do the rref.

Thanks!

6. Originally Posted by ndb

50x + 30y = 450 min
45x + 15y = 400 min

45x + 1y + 14z = 420
33x + 20y + 15z = 450
50x + 15y + 10z = 400

What the results should be? I am not sure I can do the rref.

Thanks!
Unless you show how you worked your rref of the matrices, I am not going to work them out for you. If you don't need to show your work, just put them in a calculator.