Results 1 to 4 of 4

Math Help - Linear programming model

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    142

    Linear programming model

    I have this word problem, which I really suck on it. I don't know how to put it in mathematical equation.

    Problem:Computer business.

    A computer science major and a business major decide to start a small business that builds and sells a desktop computer and a laptop computer. They buy the parts, assemble them, load the operating system, and sell the computers to other students. the costs for parts, time to assemble the computer, and profit are summarized in the following table:


    Costs of parts: (desktop)$700 & (laptop)$400
    Time to assemble(hours): (desktop) 5hrs & (laptop) 3hrs
    Profit: (desktop) $500 & (laptop) $300

    They were able to get a small business loan in the amount of $10000 to cover the costs. they plan on making these computers over the summer and selling them the first day of class. they can dedicate at most only 90hours to assembling these computers. they estimate that the demand for laptops will be at least three times as great as the demand for desktops. How many each type of computer should they make to maximize the profit? Also compute for actual demand with business loan of $12400.


    please help me out! Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member u2_wa's Avatar
    Joined
    Nov 2008
    Posts
    119
    Hello Anemori:

    Figure out the constraints:

    Let D=desktop and L=Laptop

    1. 700D+400L\leq10000(Loan)

    2. 5D+3L\leq90(Time available)

    3. 3D\leq L(Demand)

    4. Profit=$500D+$300L

    Draw the first three constraints on the graph and find the feasible region.
    Put the corner values of the feasible region in the profit equation to find the combination that gives the highest profit!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    142
    how do i draw this on a graph? how can i find points?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by Anemori View Post
    how do i draw this on a graph? how can i find points?
    1. Take inequalities posted by u2_wa and solve for one variable. I'll take L:

    700D+400L\leq10000~\implies~L\leq -\frac74 D + 25

    5D+3L\leq90~\implies~L \leq -\frac53 D + 30

    3D\leq L~\implies~L\geq 3D
    and add:
    L\geq 0 , D\geq 0

    2. Consider the equal parts of the inequalities as equations of straight lines which are the borders of the feasible region.

    3. The vertices of the feasible region are the points of intersection of the three straight lines. Calculate the coordinates of the vertices.
    Attached Thumbnails Attached Thumbnails Linear programming model-computerproduction.png  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to set up a linear programming model
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: February 12th 2011, 08:44 AM
  2. Linear programming model
    Posted in the Business Math Forum
    Replies: 2
    Last Post: May 7th 2010, 09:30 AM
  3. model linear programming problem
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: May 2nd 2010, 06:47 PM
  4. [SOLVED] Linear Programming model
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 27th 2007, 03:07 PM
  5. Replies: 5
    Last Post: September 26th 2007, 11:50 PM

Search Tags


/mathhelpforum @mathhelpforum