Marking Scheme for Midterm

1. Problem 1

   2 marks each for:
   changing form to apply dual simplex
   2 iterations
   final opt. solution

   Solution (pdf)

2. Problem 2

   • part 1:
     definition of parameters, var: 2
     objective: 2
     lower/upper bounds: 1
     constraint for stock l.e. bonds + gic: 2
     - ignored most syntax mistakes but if sets were not used (eg. the decision vars are bonds, stocks, certificates) to allow easy modification of the data deducted one mark
   • part 2:
     1 mark for adding the set "investors" or something like it.
     1 mark for providing the correct updated model.
   • part 3:
     1 mark for providing a constraint which would create some kind of diversification in the portfolio correctly (eg. forcing all investments to be more/less than some of fraction of the total)

3. Problem 3

   A single mark off for an arithmetic error. Two marks off for major mistakes relating to serious misunderstanding.
   The marks were generally quite low for Q3; average was about 6/12.

   Solution (pdf)

   There are four intervals, i.e. three breakpoints
   • range of t (four intervals):
     [-infty,-1]; [-1,3/2]; [3/2,7/3];[7/3,infty]
   • optimal solution:
     x=(0,4,6,2,0); x=(2,4,2,0,0); x=(4,2,0,0,2); x=(5,0,0,1,4);
   • objective value:
     z=16-4t; z=18-2t; z=12+2t; z=5+5t;

4. Problem 4

   1. obj. function 5
      bound constr 5
      special balance constr. 5
      units should match on left and right of inequalities/constraints emphasis: that checking units makes a big difference!! define variables carefully, i.e. document!
   2. document carefully; check units
   3. +1 for all space/wt used up ... +1 for why, i.e. C.S.