OPERATIONAL RESEARCH. FIRST IN CLASS TEST
Consider the following Linear Programming problem
0 0
33
0
Subject to
Maximise
21
21
21
210
0
≥≥
≤−
≤+−
+=
xx
xx
xx
xxx
x
Graphically represent the feasible region for the solution of the problem. 10 marks.
Indicate where in the feasible region could the optimal solution be found. 10 marks.
Evaluate the objective function in all the possible optimal points and find the optimum. 20
marks.
Add slack variables and write the SIMPLEX tableau LP associated with the problem. 10 marks.
Choose and initial basic feasible solution, and apply the optimality and the feasibility rules to
move one step towards the optimal solution. Optimality rule 10 marks. Feasibility rule 10
marks. Explain what you have done. 10 marks.
Solve the problem and check that your final solution coincides with the solution you obtained
using the graphical method. One Simplex iteration 10 marks. Correct solution found 10
marks.
Resolution:
ܺ
= ܺ
ଵ
+ ܺ
ଶ
−ܺ
ଵ
+ ܺ
ଶ
= 0
3ܺ
ଵ
− ܺ
ଶ
= 3
The solution can be found in the corners of
the feasible region (A, B, C)
A (0,0): ܺ
= ܺ
ଵ
+ ܺ
ଶ
= 0 + 0 = 0
B (0,1): ܺ
= ܺ
ଵ
+ ܺ
ଶ
= 0 + 1 = 1
C (
ଷ
ଶ
,
ଷ
ଶ
): ܺ
= ܺ
ଵ
+ ܺ
ଶ
=
ଷ
ଶ
+
ଷ
ଶ
=
ଶ
= 3
In this case, the optimal option is the corner
C because it gives us a value of 3 (the higher
value of the three corners)
