Matrix word problem- Precalculas

thearn

1. The problem statement, all variables and given/known data
Factory A and B sent rice to store 1 and 2. Factory A sent 10 loads and factory B sent 24. Store 1 used 17 loads and store 2 used 17 loads. It cost 200$ per load to ship from factory A to store 1. It cost 350$ per load to ship from factory A to store 2. It cost 300$ per load to ship from factory B to store 1. It cost 250$ per load from factory B to store 2. A tiotal of 8350$ was spent on shipping. How many loads were shipped from each factory to each store.


2. Relevant equations
None


3. The attempt at a solution
The problem that I am having is setting up the equations to create a matrice that can accurately reflect the problem.
some scribbles were
200x+350y+300z+350E=8350$
x+y+z+e=34

Mark44

Start by defining what your variables mean.
What do x, y z, E, and e represent?

After you do that, see if you can translate the statements in English in the problem to mathematical equations.

thearn

So I now have
200A1+350A2+300B1+250B2=8350
A1+0+B1+0=17
0+A2+0+B2=17
A1+A2+B1+B2=34
Defining the variables gives me.
A1= loads from factory A to store 1
B1= Loads from factory B to store 1
A2= Loads from factory A to store 2
B2= Loads from factory B to store 2
The answer came out with 27, 17, -10, and 0. So it's clear I set it up incorrectly.

Mark44

Now that you have identified some variables, let's start translating the problem statement.

This can be translated into two equations.

One of them is
A1 + A2 = 10

Do you understand what this is saying?
If so, what other equation can we get from the sentence above?

thearn

B1 + B2 = 24
A1 + A2 = 10
yes, what it is saying is that Loads from factory B to store1 + Loads from factory B to store2 = 24 loads. Same concept with A1 + A2 = 10

Ray Vickson

If A1, A2, B1, B2 are the factory-store shipments (in obvious labelling), we have
[tex] \begin{array}{l}A1+A2 = 10\\
B1 + B2 = 24\\
A1+B1 = 17\\
A2 + B2 = 17
\end{array}[/tex]
Here, you have 4 unknowns and 4 equations, but if you try to solve them you will find that you can't get a complete solution. Basically, one of the 4 equations follows from the other three, so you really have only 3 independent equations.

You need a 4th, independent, equation, and that is where the cost information comes in. So, omit one of the equations above and replace it by the cost equation---then solve.

RGV

thearn

thanks that got it done.