CO 355 Mathematical Optimization (Fall 2010)
Assignment 1
Due:
Tuesday September 28th, in class.
Policy.
No collaboration is allowed. You may only use the course notes / textbook and the lecture slides.
Every other resource that you might stumble upon must be properly referenced. You are welcome to seek
help from the current instructor and TAs for CO 355.
Question 1:
(15 points)
(You do not need to be very rigorous for this question.)
In class we claimed the “Fundamental Theorem of LPs”: every linear program either has an optimal
solution, is unbounded, or is infeasible.
Consider the following linear program in
R
2
, whose objective function has not yet been speciﬁed.
min
ax
+
by
s.t.
x

y
≤
2

2
x
+
y
≤
2
x
+
y
≥
2
(a):
Find an objective function (i.e., values of
a
and
b
) for which the linear program has a unique
optimal solution.
(b):
Find an objective function for which the linear program has inﬁnitely many optimal solutions.
(c):
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 Winter '10
 Harvey
 Operations Research, Optimization, objective function, linear program

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