Results 1 to 4 of 4

Math Help - Please help me to solve the followings linear programming problems. Thanks.

  1. #1
    Junior Member
    Joined
    Oct 2006
    From
    canada
    Posts
    68

    Please help me to solve the followings linear programming problems. Thanks.

    Hello.
    could somebody please help me to solve this exercise?

    Maximize:
    F = 7x + 10y subject to:
    14x -5y ≥ 98
    8x + 10y ≥ 100

    thanks.
    Last edited by jhonwashington; November 21st 2009 at 09:37 PM. Reason: I already solved the other excercises..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by jhonwashington View Post
    Hello.
    could somebody please help me to solve this exercise?

    Maximize:
    F = 7x + 10y subject to:
    14x -5y ≥ 98
    8x + 10y ≥ 100

    thanks.
    You can create the tableau

    <br />
\begin{array}{|c| c c c c | c|}\hline<br />
\phantom{x} & x & y & s_1 & s_2 & \phantom{x}\\\hline<br />
s_1 & -14 & 5 & 1 & 0 & -98\\ s_2 & -8 & -10 & 0 & 1 & -100\\\hline \phantom{x} & -7 & -10 & 0 & 0 & 0\\\hline<br />
\end{array}<br />

    and then apply the dual simplex method.

    If you're not familiar with this method, you can introduce slack variables and artifical variables to create a different tableau (which I leave for you to set up). Then use the two phase method to solve the LP problem.

    Does this make sense? Can you take it from here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    Quote Originally Posted by jhonwashington View Post
    Hello.
    could somebody please help me to solve this exercise?

    Maximize:
    F = 7x + 10y subject to:
    14x -5y ≥ 98
    8x + 10y ≥ 100

    thanks.
    There is no maximum. You can take x and y are large as you like and so have F as large as you like. Are you sure the conditions are not 14x- 5y\le 98 and 8x+10y\le 100?
    If so:

    For a problem with only two variables, it is not necessary to use the tableau method.

    Draw the lines 14x- 5y= 98 and 8x+ 10y= 100. Those, together with the condition that neither x nor y is negative, define the "feasible region"- the possible values for x and y. The fundamental theorem of "linear programming" is that the max or min of a linear object function, assuming there is one, must occur at a vertex of the feasible region. The vertices will be where the lines intersect and where they intersect the axes. find the (x,y) coordinates of those points and evaluate 7x+ 10y at those points.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Nov 2009
    From
    Lebanon
    Posts
    26
    this equations dont need the simplix method you can solve it easly yousing the graphing method
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] How to solve a linear programming question with "mixing
    Posted in the Algebra Forum
    Replies: 0
    Last Post: November 27th 2011, 06:01 AM
  2. Replies: 5
    Last Post: February 8th 2011, 08:14 PM
  3. Solve the linear programming problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 10th 2010, 11:16 AM
  4. Asking for linear programming problems
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: October 26th 2008, 08:37 AM
  5. 2 linear programming problems can any1 explain please?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: February 21st 2007, 11:44 AM

Search Tags


/mathhelpforum @mathhelpforum