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Thread: Linear programming model

  1. #1
    Jan 2010

    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!
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  2. #2
    Member u2_wa's Avatar
    Nov 2008
    Hello Anemori:

    Figure out the constraints:

    Let D=desktop and L=Laptop

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

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

    3.$\displaystyle 3D\leq L$(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!
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  3. #3
    Jan 2010
    how do i draw this on a graph? how can i find points?
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  4. #4
    Super Member
    earboth's Avatar
    Jan 2006
    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:

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

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

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

    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.
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