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Math Help - Linear Algebra-Matricies/Word Problems?

  1. #1
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    Linear Algebra-Matricies/Word Problems?

    Find the possible number of batches of each product that can be made such that all of the available materials are used up.

    1) Nutrina Feeds manufactures the dog foods RUFF, FLUFF, and PROWL from a blend of wheat and soybeans. A batch of RUFF uses 1000 pounds of wheat and 3000 pounds of soybeans; a batch of FLUFF uses 2000 pounds of wheat and 7000 pounds of soybeans; and a batch of PROWL uses 2000 pounds of wheat and 5000 pounds of soybeans. Suppose that there are 15,000 pounds of wheat and 50,000 pounds of soybeans on hand.

    This is the answer on the back. But, word problems are hard to solve for me.

    Answer

    Ruff
    5
    1
    Fluff
    5
    6
    Prowl
    0
    1

    The number represent the batches....
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by snakeman11689 View Post
    Find the possible number of batches of each product that can be made such that all of the available materials are used up.

    1) Nutrina Feeds manufactures the dog foods RUFF, FLUFF, and PROWL from a blend of wheat and soybeans. A batch of RUFF uses 1000 pounds of wheat and 3000 pounds of soybeans; a batch of FLUFF uses 2000 pounds of wheat and 7000 pounds of soybeans; and a batch of PROWL uses 2000 pounds of wheat and 5000 pounds of soybeans. Suppose that there are 15,000 pounds of wheat and 50,000 pounds of soybeans on hand.

    This is the answer on the back. But, word problems are hard to solve for me.

    Answer

    Ruff
    5
    1
    Fluff
    5
    6
    Prowl
    0
    1

    The number represent the batches....
    Let the numbers of batches of each product be R, F and P. Then you want to use all the stock so:

    1000 R + 2000 F + 2000 P = 15000

    3000 R + 7000 F + 5000 P = 50000

    Now you have to find triples (R,F,P) of integers which satisfy these equations.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Let the numbers of batches of each product be R, F and P. Then you want to use all the stock so:

    1000 R + 2000 F + 2000 P = 15000

    3000 R + 7000 F + 5000 P = 50000

    Now you have to find triples (R,F,P) of integers which satisfy these equations.

    RonL
    I got that, but what do i do from there. Divide both rows by 100, and then put it in row echelon form..?
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    Let the numbers of batches of each product be R, F and P. Then you want to use all the stock so:

    1000 R + 2000 F + 2000 P = 15000

    3000 R + 7000 F + 5000 P = 50000

    Now you have to find triples (R,F,P) of integers which satisfy these equations.

    RonL
    Quote Originally Posted by snakeman11689 View Post
    I got that, but what do i do from there. Divide both rows by 100, and then put it in row echelon form..?
    Divide through by 1000, to get:

    1 R + 2 F + 2 P = 15

    3 R + 7 F + 5 P = 50

    Now subtract 3 times the first from the second to get

    F-P=5.

    From the first equation we know 0<=P<=7, so now go through the posibilities
    for P finding the corresponding F's. Then check in the first equation to see if
    there is a non-negative R to go with the P and F's.

    This will leave you with a list of feasible solutions.

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    Divide through by 1000, to get:

    1 R + 2 F + 2 P = 15

    3 R + 7 F + 5 P = 50

    Now subtract 3 times the first from the second to get

    F-P=5.

    From the first equation we know 0<=P<=7, so now go through the posibilities
    for P finding the corresponding F's. Then check in the first equation to see if
    there is a non-negative R to go with the P and F's.

    This will leave you with a list of feasible solutions.

    RonL
    Ok... I got the F-P=5, However, when i set P=0, and P=1, I can't seem to get Ruff equal to R=5, and R=1, but i got the right answer for Fluff.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by snakeman11689 View Post
    Ok... I got the F-P=5, However, when i set P=0, and P=1, I can't seem to get Ruff equal to R=5, and R=1, but i got the right answer for Fluff.

    When P=0, F=5 from F-P=5

    Then as 1 R + 2 F + 2 P = 15 = R+10, so R=5, which is the first quoted solution.

    RonL
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