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Math Help - linear programming

  1. #1
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    linear programming

    A logging firm gets logs from its supplier of  10' and  20' (and can get as many of each as he needs). The firm needs to produce logs of lengths  5' ,  7' , and  9' and needs  1000 ,  3000 , and  2000 of these lengths respectively. The firm needs to know how to cut the logs up so the total excess is minimized. How should the firm cut up the logs? The firm can stockpile any excess logs of  5' ,  7' , or  9' lengths at no cost.



    So let  x_{1} = number of  5' logs cut,  x_2 = number of  7' logs cut and  x_3 = number of  9' logs cut.

    Then we want to minimize:  \text{max} \ z = x_{1}-x_{2}-x_{3} subject to constraints  x_1 \geq 0, \ x_2 \geq 0, \ x_3 \geq 0 .

    Can you rule out the  10' case altogether because  5' + 5' = 10' (excess = 0)? Then formulate as  \text{min} \ z  = 20-x_{1}-x_{2}-x_{3} s.t. the same constraints as above?

    Is this correct?
    Last edited by particlejohn; September 10th 2008 at 07:14 AM.
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