\Opgave 1

a) Let x_1 be the number of hams sold as fresh
   Let x_2 be the number of hams smoked on regular time
   Let x_3 be the number of hams smoked on overtime
   Let x_4 be the number of bellies sold as fresh
   Let x_5 be the number of bellies smoked on regular time
   Let x_6 be the number of bellies smoked on overtime
   Let x_7 be the number of picnic hams sold as fresh
   Let x_8 be the number of picnic hams smoked on regular time
   Let x_9 be the number of picnic hams smoked on overtime

   max 8 x1 + 14 x2 + 11 x3 + 4 x4 + 12 x5 + 7 x6 + 4 x7 + 13 x8 + 9 x9

   s.t 1 x1 +  1 x2 +  1 x3                                             <= 480
                              1 x4 +  1 x5 + 1 x6                       <= 400
                                                    1 x7 +  1 x8 + 1 x9 <= 230
               1 x2                +  1 x5               +  1 x8        <= 420
                       1 x3                + 1 x6                + 1 x9 <= 250

  notice that the model is TU as 
  - all coefficients are 0,1,-1
  - if we split the rows after the third inequality, then we have:
    if two coefficients in the same column have the same sign +1, 
    then they belong to two different sets.
  thus we will always get integer-solutions to the problem as long as
  the right-hand sides are integers.