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Math Help - Optimization problem #3

  1. #1
    MHF Contributor alexmahone's Avatar
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    Optimization problem #3

    A printing company has eight presses, each of which can print 3600 copies per hour. It costs $5.00 to set up each press for a run and 10+6n dollars to run n presses for 1 h. How many presses should be used to print 50,000 copies of a poster most profitably.
    Last edited by mr fantastic; July 22nd 2010 at 11:20 PM. Reason: Edited title.
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  2. #2
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    Profit is revenue minus cost. In this case, revenue is presumed to be a fixed value because the number of copies is fixed at 50,000. Therefore, maximizing profit in this problem is the same as minimizing cost.

    Can you come up with a solution that minimizes the total cost?
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by drumist View Post
    Can you come up with a solution that minimizes the total cost?
    I wasn't able to come up with a formula for the total cost.
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    Quote Originally Posted by alexmahone View Post
    A printing company has eight presses, each of which can print 3600 copies per hour. It costs $5.00 to set up each press for a run and 10+6n dollars to run n presses for 1 h. How many presses should be used to print 50,000 copies of a poster most profitably.
    Let x be the number of presses used.
    Firstly, we have to assume that
    (i)the work will be finished in one run;
    (ii)all presses begin to run at the same time;
    Then, we can have the following formula that denotes the cost:
    5x+(10+6x)(50000/x)/3600
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