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Linear programs and the simplex algorithm
1.1
[25 marks total]
[7 marks]
The following figure is a graphical presentation of a linear program in standard form with slack
variables x3 , x4 , and x5 . As in the lecture, the darker area of a black solid line marks the area
where xi ≥ 0.
Your task is to list all bases that correspond to basic feasible solutions. Give a detailed reason
for your answer.
x5 = 0
x3 = 0
x4 = 0
c
x2 = 0
x1 = 0
1.2
[10 marks]
Given the following linear program in dictionary format, decide whether or not the optimal
objective function value is 17. Give a detailed reason for your answer.
max ζ
subject to x1
x4
x2
1.3
= 17 +x3 −4x5
= 1 −x3
=
−x3
+x5
= 1 +x3 −x5
[8 marks]
For some linear programs it is not obvious if they have any feasible solutions. Describe a
method that can answer whether or not a linear program has a feasible solution.
PAPER CODE COMP331
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