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Math Help - Formulating an Integer Programming problem

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    Formulating an Integer Programming problem

    A manufacturer can sell product 1 at a profit of $2/unit and product 2 at a profit of $5/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture 1 unit of product 2. A total of 120 units of raw material are available. If any of product 1 is produced, a setup cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $20 is incurred. Formulate an IP to maximize profits. For computational simplicity you can assume that it is allowed to produce fractions of product 1 or product 2 (so the numbers of products do not have to be integers).
    Last edited by CaptainBlack; April 25th 2009 at 01:13 AM.
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  2. #2
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    Quote Originally Posted by jlt1209 View Post
    A manufacturer can sell product 1 at a profit of $2/unit and product 2 at a profit of $5/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture 1 unit of product 2. A total of 120 units of raw material are available. If any of product 1 is produced, a setup cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $20 is incurred. Formulate an IP to maximize profits. For computational simplicity you can assume that it is allowed to produce fractions of product 1 or product 2 (so the numbers of products do not have to be integers).

    Let x be the number of units of product 1 produced, and y be the number of units of product 2.

    The objective is the profit:

    O=2x+5y-10I(x)-20I(y)

    where I(.) is the indicator function which is 1 if its argument is greater than 0 and 0 otherwise (alternativly introduce two 0-1 variables to handle the set up costs).

    The nonnegativity constraints are that x\ge 0 , y\ge 0 and the materials constraint is:

    3x+6y \le 120

    CB
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