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Math Help - linear programming

  1. #1
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    linear programming

    Hi, im not sure where this goes but imma just go ahead and post it here.

    Question 3 Book Sales
    Solve by graphing: O'Hagan Bookworm Booksellers buys books from two publishers. Duffin House offers a package of 5 mysteries and 5 romance novels for $50, and Gorman Press offers a package of 5 mysteries and 10 romance novels for $150. O'Hagan wants to buy at least 2,500 mysteries and 3,500 romance novels, and he has promised Gorman (who has influence on the Senate Textbook Committee) that at least 25% of the total number of packages he purchases will come from Gorman Press. How many packages should O'Hagan order from each publisher in order to minimize his cost and satisfy Gorman? What will the novels cost him?
    Answer: Buy 420 packages from Duffin Publishers and 140 from Gorman Press for a total cost of $42,000.
    So far i got: (x = Duffin ; y= Gorman)
    5x+5y>=2500
    5x+10y>=3500
    50x+150y=c

    Can you guys help me with the bolded part.
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    The total number of packages is x+y. You want y to be at least a quarter of the total. So y\geqslant\tfrac14(x+y), which you can simplify to 3y-x\geqslant0.
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