Uitwerking Practical 1 Decision Science

Decision Science 1, Computer Practical,
Practical work, Week 1 P1 Pair number: 14

Name: Dennis van den Berg Reg nr: 1 0 4 8 1 6 8

Name: Lars van der Horst Reg nr: 1 0 4 9 5 2 8

Exercise 1 The following questions are based on exercise 1 (farmer’s problem).
1-b1 Formulate the problem as a linear programming problem. Implement it in Fico Xpress-IVE (use standard.mos
as a starting point). Compare the optimal solution with the solution you found in your homework (question
a1).

MaxW=4500*x1+5000*x2+6000*x3
x1 <= 5
x2 <=3,3333
x3 <= 2,5
2x1 + 24x2 + 158x3 <= 350
25x1 + 20x2 + 5x3 <=150


Grain 2.99 ha
Potatoes 3.33 ha
Sugar beets 1.67ha
Profit € 40.188
Binding constraints
Available
labour
hours,
potatoes


A1: Additional labour cost spring
A2: Additional labour cost autumn

MaxW=4500*x1+5000*x2+6000*x3 – 33 * (A1+A2)
x1 <= 5
x2 <=3,3333
x3 <= 2,5
2x1 + 24x2 + 158x3 <= 350 +A1
25x1 + 20x2 + 5x3 <=150 +A2



1-b2 Give the adapted model formulation for question b2.
Additional decision variables (if any):
A1: Additional labour cost spring
A2: Additional labour cost autumn

Changes in the formulation of the objective function (if any): - 33* (A1+A2)

Changes in the formulation of the constraints (if any):
2x1 + 24x2 + 158x3 <= 350 +A1
25x1 + 20x2 + 5x3 <=150 +A2

Grain 5 ha
Potatoes 3.33 ha
Sugar beets 1.67ha
Profit € 47396,91