## Matrix word problem- Precalculas

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

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Mentor
 Quote by 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
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.

 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.

Mentor

## Matrix word problem- Precalculas

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

 Factory A sent 10 loads and factory B sent 24.
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?

 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

Recognitions:
Homework Help
 Quote by 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
If A1, A2, B1, B2 are the factory-store shipments (in obvious labelling), we have
$$\begin{array}{l}A1+A2 = 10\\ B1 + B2 = 24\\ A1+B1 = 17\\ A2 + B2 = 17 \end{array}$$
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

 thanks that got it done.

 Tags matrice, matrix, matrix algebra, matrix application, matrix word problem