Results 1 to 3 of 3

Math Help - Solving Systems by Matrix Reduction

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    15

    Solving Systems by Matrix Reduction

    Could someone kindly provide me with the process of how I can solve the following word problem using matrices?

    Question: A firm produces three products, A, B and C that require processing by three machines, I, II, III. The time in hours required for processing one unit of each product by the three machines is given by the following table:


    A B C
    I 3 1 2

    II 1 2 1

    III 2 4 1

    Machine I is available for 490 hours, machine II is available for 310 hours, and machine III for 560 hours. Find how many units of each product should be produced to make use of all the available time on the machines.

    I am sorry, I don't know how to post a proper table for my question. But in the table above IA corresponds to entry 3, IB = 1, IC = 2, IIA=1, IIB=2, IIIC=1, IIIA=2, IIIB=4, IIIC=1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,751
    Thanks
    651
    Hello, alisheraz19!

    I'm not sure that matrices is the best way to go . . .


    A firm produces three products: A, B, C
    that require processing by three machines: I, II, III.
    The time in hours required for processing one unit of each product
    by the three machines is given by the following table:

    . . <br />
\begin{array}{c||c|c|c||c|}<br />
& A & B & C & \text{Total} \\ \hline\hline<br /> <br />
I & 3 & 1 & 2 & 490 \\  \hline<br /> <br />
II & 1 & 2 & 1 & 310   \\  \hline<br />
III & 2 & 4 & 1 & 560 \\ \hline \end{array}

    Macine I is available for 490 hours,
    machine II is available for 310 hours,
    machine III for 560 hours.

    Find how many units of each product should be produced
    to make use of all the available time on the machines.
    Let: . \begin{Bmatrix} a &=& \text{number of A's} \\ b &=& \text{number of B's} \\ c &=& \text{number of C's} \end{Bmatrix}

    We have three inequalities: . \begin{array}{ccc}a + b + 2c & \leq & 490 \\ a + 2b + c & \leq & 310 \\ 2a + 4b + c & \leq & 560 \end{array}


    Solve the system of equations: . \begin{array}{ccc} 3a + b + 2c &{\color{red}=}& 490 \\ a + 2b + c &{\color{red}=}& 310 \\ 2a + 4b + c &{\color{red}=}& 560\end{array}

    . . and we get: . \begin{Bmatrix}a\;=\;98 \\ b \;=\;76 \\ c \;=\;60\end{Bmatrix}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    15

    Question asks for Matrix

    I'm sorry, I wasn't very clear in my description.

    The question in my textbook asks to use matrix reduction to solve the matrix.

    I know how to reduce matrices, I just don't know (in this particular question) how to get to the matrix which needs to be reduced (ie. the equation for the matrix that must be reduced to solve the quesion)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 9th 2011, 02:50 AM
  2. Replies: 2
    Last Post: February 19th 2011, 06:57 AM
  3. matrix row reduction solution question..
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 16th 2010, 05:41 AM
  4. Matrix Row Reduction
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 6th 2008, 10:38 PM
  5. Replies: 3
    Last Post: October 11th 2006, 09:15 PM

Search Tags


/mathhelpforum @mathhelpforum