Uitwerking Practical 2 Decision Science

Decision Science 1, Computer Practical,
Practical work, Week 2 P2 Pair number: 14

Name: Lars van der Horst Studentnumber: 1 0 4 9 5 2 8
Name: Dennis van den Berg Studentnumber: 1 0 4 8 1 6 8

Watch the Introduction clip to P2

Exercise 1
Open the existing file <DS1_01 farmer.mos> (see Brightspace)

1-d2 Determine the rank r(A) for problem b1 (without additional casual labour) in standard form (Ax=b).
Explain!
r(A) <= min(m,n) --> min (6,9) <= 6


1-d3 Give the optimal basic solution x=
( )
xB
xN
(without additional casual labour).

(Xb) = Alle positieve getallen
(Xn) = Alles wat 0 is

MaxW=4500*x1+5000*x2+6000*x3
1: x1 +y1 = 5
2: x2 +Y2 =3,3333
3: x3 +Y3 = 2,5
4: 2x1 + 24x2 + 158x3 +Y4 = 350
5: 25x1 + 20x2 + 5x3 + Y5 =150
6: X1 + X2 + X3 +Y6 = 10
X1, X2, X3 >= 0

xB’ = (XG XP XB Y1 Y3 Y6) = (3.00 3.33 1.67 4.00 3.32 2.00)
xN’ = (Y2 Y4 Y5) = (0 0 0)

1-d4 Which of the constraints are binding and which are non-binding?
Constraint Binding / Non-binding
1 Non binding
2 Binding
3 Non binding
4 Binding
5 Binding
6 Non binding

1-d5 After extending the problem with additional labour at $ 33 per hour (see question b.) the number of basic
variables in the optimal basis will:
1. increase
2. be equal
3. decrease
Explain your answer!
Be equal, because there are no new constraints with the new labour.


1-d6 Give the vector of non-basic variables xN for the problem in question b2. (additional labour is allowed).

MaxW=4500*x1+5000*x2+6000*x3 – 33 * (A1+A2)
1: x1 +y1 = 5
2: x2 +Y2 =3,3333
3: x3 +Y3 = 2,5
4: 2x1 + 24x2 + 158x3 +Y4 = 350 + A1
5: 25x1 + 20x2 + 5x3 + Y5 =150 + A2
6: X1 + X2 + X3 +Y6 = 10