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Matrix word problem- Precalculas

  1. May 2, 2012 #1
    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
     
  2. jcsd
  3. May 2, 2012 #2

    Mark44

    Staff: Mentor

    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.
     
  4. May 2, 2012 #3
    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.
     
  5. May 2, 2012 #4

    Mark44

    Staff: Mentor

    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?
     
  6. May 2, 2012 #5
    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
     
  7. May 2, 2012 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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
     
  8. May 3, 2012 #7
    thanks that got it done.
     
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