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Math Help - Calculating maximum profit

  1. #1
    Newbie
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    Sep 2009
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    Calculating maximum profit

    A game company is developing two new games, a board game and a mechanical game. Each board game requires \frac{1}{2}h to manufacture, \frac{1}{2}h to assemble, and \frac{1}{4}h to inspect and package. Each mechanical game requires 1h to manufacture, \frac{1}{2}h to assemble, and \frac{1}{2}h to inspect and package. In a given week there are 40h available for manufacturing, 32h available for assembly, and 18h for inspection and packaging. Suppose the profit on each board game is $10 and the profit on each mechanical game is $15. How many of each game should be produced each week for maximum profit?

    I know how to maximize a function, but I have no idea how to set up the equation for this problem.
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  2. #2
    Junior Member
    Joined
    Oct 2009
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    Alright, well I think we'd need to set up a series of equations:
    First lets just look at the time we have for manufacturing
    Let x= amount of board games and y=amount of mechanical games
    so:
    40=.5x+y
    Since we have 40 total hours, each board game takes 1/2 an hour and each mechanical takes one full hour.

    Next for the assembly, use the same method:
    32=.5x+.5y

    Next for the inspection/packaging:
    18=.25x+.5y

    Lastly for the amount of profit (P):
    P=10x+15y

    Hopefully that helped...
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