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Math Help - Linear programming - problem

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    38

    Linear programming - problem

    Hi please give me a help to find out the answer for the following linear programing question

    There are two products x1 and x2 manufactured on two machines M1 and M2.
    Product x1 requires 3 hours on machine M1 and half and hour on machine M2. Product
    x2 requires two hours on machine M1 and one hour on machine M2. Total available
    capacity on machine M1 is six hours and that on machine M2 is four hours. Each unit
    of x1 has an incremental profit of Rs.12/= and each unit of x2 an incremental profit of
    Rs.4/=.
    (a) Formulate the Primal problem.
    (b) Write the dual problem to the above primal problem.
    (c) Solve the dual problem and by using it find the solution for the primal problem.

    The above part (a) is I done as follows; Mathematical formulation is

    To maximize : Z=12a+4b --> Equation 01

    Subject to constraints :

    3a+2b \le 6 --> Equation 02

    \frac {1}{2} a+b \le 4 --> Equation 03

    a \ge 0, b \ge 0 --> Equation 04

    If the above it true plz give me a help to find the other part (b) and (c) or help me to find the answer
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  2. #2
    Newbie
    Joined
    Dec 2009
    Posts
    5
    Your primal problem is correct!

    Here is part (b)

    The dual problem is:

    Min TC = 6u1 + 4u2
    st. 3u1 + 0.5u2 >= 12
    2u1 + u2 >= 4
    u1, u2 >= 0

    Try part (c) yourself
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