Results 1 to 4 of 4

Math Help - Linear Programming Problem

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    2

    Linear Programming Problem

    Hey guys, I have been trying to teach myself some basic concepts of operations research. I have run across a problem that has been giving me some trouble. Here it is:

    A supermarket store manager needs to determine how much to stock of two brands of soda: PC and CC, for Super Bowl Sunday. The store needs to tell the suppliers how many “units” are available and the suppliers then stock the store with their product. Units consist of different flavors and sizes depending on what the suppliers think will sell best. Fractions of units are OK. The store’s makes a profit margin of 15 cents for each unit of PC and 10 cents for each unit of CC. In the soda aisle, there is a maximum of 36 linear feet of shelf space: each unit of PC takes up 9 linear feet of shelf space and each unit of CC takes up 4 linear feet of shelf space. In the end displays, there is a 20 linear feet of display space available: each unit of PC takes up 4 linear feet of display space and each unit of CC takes up 4 linear feet of display space. In other words, 1 unit of PC will require 9 feet in the soda aisle plus 4 feet in the end display area.

    I know its a maximization problem and the objective function is Z = .15p + .1c where p is the decision variable for units of PC and c is the decision variable for units of CC.

    I start to get a little confused with finding the constraints of the problem. So far I have

    9p + 4c <= 36
    4p + 4c <= 20

    Are there any more constraints? The last sentence confuses me. Does the last sentence mean that I should have additional constraints?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by tbird0041 View Post
    Are there any more constraints?
    what about p\geq 0 , c\geq 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    2
    yes I would agree with that, I forgot to put those two constraints in the problem because I normally just assume nonegativity, other than those 4 would there be anymore constraints to add?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    I think you have them all, now to maximise z 'profit', test the corner points of the feasible region against the objective function.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear programming problem.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 2nd 2011, 01:08 AM
  2. Linear programming problem
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: August 25th 2010, 07:57 AM
  3. linear programming problem
    Posted in the Business Math Forum
    Replies: 2
    Last Post: March 9th 2010, 01:10 PM
  4. Linear Programming problem
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: January 4th 2009, 09:27 AM
  5. linear programming problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 31st 2007, 07:02 AM

Search Tags


/mathhelpforum @mathhelpforum