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Math Help - Linear Programming Help

  1. #1
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    Linear Programming Help

    Now I don't need you guys to do my homework for me; however, I am a little stumped

    Xara Stores in Canada imports the designer-inspired clothes it sells from suppliers in China and Brazil. Xara estimates that it will have 45 orders in a year, and it must arrange to transport orders (in less-than-full containers) by container ship with shippers in Hong Kong and Buenos Aires. The shippers Xara uses have a travel time of 32 days from Buenos Aires and 14 days from Hong Kong, and Xara wants its orders to have an average travel time of no more than 21 days. About 10% of the annual orders from the shipper in Hong Kong are damaged, and the shipper in Buenos Aires damages about 4% of all orders annually. Xara wants to receive no more than 6 damaged orders each year. Xara does not want to be dependent on suppliers from just one country, so it wants to receive at least 25% of its orders from each country. It costs $3,700 per order from China and $5,100 per order to ship from Brazil. Xara wants to know how many orders it should ship from each port in order to minimize shipping costs.
    a) Formulate a linear programming model for this problem.

    Okay so, I'm not totally clueless here

    If I let X = shipments from China, and Y = shipments from Brazil, my cost minimization is

    3700X + 5100Y = Min Cost

    Also, I assume one of the constraint equations is
    .1X + .04Y < 6

    At this point I am stumped. My prof told me that one equation will be .75X - .25Y > 0, but I do not understand how I can graph that line

    Any help is appreciated
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  2. #2
    MHF Contributor
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    Re: Linear Programming Help

    You have the following constraints:

    x + y = 45
    (14x + 32y)/45 <= 21
    0.1x + 0.04y <= 6
    x >= 0.25 * 45
    y >= 0.25 * 45

    You need to minimize 3700x + 5100y, which gives the same x and y as minimizing 3.7x + 5.1y.
    Thanks from ADRossi
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