Results 1 to 8 of 8

Math Help - Linear Programming and Systems! HELP!

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Miami
    Posts
    5

    Linear Programming and Systems! HELP!

    This problem is so hard. I can't figure it out! I've been on it for almost an hour and I'm in desperate need of help ):
    "A gaming manufacturing company has developed a new gaming system. To produce the new system, they plan on using resources in two manufacturing plants. The table gives the hours needed for three tasks. For both plants combined, the company has allocated the following resources on a weekly basis: 1700 h of motherboard production, 1800h of technical labor, and 2400 h of general manufacturing. The first plant earns a profit of $90 per gaming system and the second plant earns $70 per system.

    Resources Plant 1 (Hours per system) Plant 2 (hours per system)
    Motherboard Production 9 1
    Technical Labor 9 3
    General manufacturing 4 8
    Use the information above to determine how many gaming systems the company should make in each plant to maximize profit.
    1. Create an objective function for the profit P that the company can earn. Let x represent the number of gaming systems that will be made in Plant 1, and let y represent the number of gaming systems that will be made in plant 2.
    (My answer - P(x,y)=90x +70y

    2. Write a constraint function for each of the resources and for any contextual contraints that you identify. (Hint. THere are 5 of these, 2 are common sense)
    (What I have x_>0 & y_>0) I NEED HELP WITH THIS!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: Linear Programming and Systems! HELP!

    I think your problem statement is a little vague. "Let x be the number of gaming systems that will be made in plant 1"-- in what time period? A day? A week? A year? Based on other information, I think we are supposed to assume the time period is a week. Then the parts of the problem begin to fit together. With this assumption, the number of hours for motherboard production per week is

     9x + 1y

    so we must have

    9x + 1y \le 1700

    The other constraints are similar.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Miami
    Posts
    5

    Re: Linear Programming and Systems! HELP!

    Well, I think it's the hours like 1700,1800, and 2400
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2012
    From
    Miami
    Posts
    5

    Re: Linear Programming and Systems! HELP!

    And the constant u listed is the one I had assumed before asking this.
    I have 9x +1y <_ 1700
    9x+3y<_ 1800
    4x +8y <_ 2400
    But when I solved for y and put in my graphing calculator it was a big mess
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: Linear Programming and Systems! HELP!

    Don't try to "solve for y" in problems like this. Did the problem statement ask for you to find the optimal solution? If not, you have met the requirements of the exercise.


    There is an algorithm for finding the optimal solution in this type of problem, but the impression I get from reading your post is that you haven't studied it yet.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2012
    From
    Miami
    Posts
    5

    Re: Linear Programming and Systems! HELP!

    Yeah, this is alg 2 hons. But that's not the whole problem.

    3. Graph the constraint functions. Then use systems of equations to find the vertex points of the feasibility region
    4. Which vertex point maximizes profit with the given constraints?
    5. What is the max profit that the company can make with the given constraints? How many gaming systems should each plant make to maximize profit?
    I know how to do all of this, but I Just can't figure out what the constraint function would be!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: Linear Programming and Systems! HELP!

    Quote Originally Posted by helpmemathhh View Post
    Yeah, this is alg 2 hons. But that's not the whole problem.

    3. Graph the constraint functions. Then use systems of equations to find the vertex points of the feasibility region
    4. Which vertex point maximizes profit with the given constraints?
    5. What is the max profit that the company can make with the given constraints? How many gaming systems should each plant make to maximize profit?
    I know how to do all of this, but I Just can't figure out what the constraint function would be!
    It's constraint functions (plural), not constraint function (singular). The constraint functions are

    9x + 1 y = 1700

    etc. Just change all the inequalities you listed into equalities.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Oct 2012
    From
    Miami
    Posts
    5
    nvm I figured out how to do it
    Last edited by helpmemathhh; October 11th 2012 at 02:41 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: February 13th 2011, 12:40 PM
  2. Help me with linear programming
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 13th 2011, 04:52 PM
  3. Replies: 7
    Last Post: August 30th 2009, 11:03 AM
  4. Replies: 1
    Last Post: November 17th 2008, 04:18 AM
  5. Linear Programming
    Posted in the Calculus Forum
    Replies: 0
    Last Post: May 6th 2008, 09:52 PM

Search Tags


/mathhelpforum @mathhelpforum