M
ASSACHUSETTS
I
NSTITUTE OF
T
ECHNOLOGY
15.053 – Optimization Methods in Management Science (Spring 2007)
Recitation 2, February 15
th
and February 16
th
, 2007
Problem 1: LP Geometry
You are given the following LP:
12
1
2
Maximize
2
s.t.

2
3
0
0
xx
x
x
−
+
≥
−
≤
≥
≥
Part A:
Find the solution to this LP using the Geometric Method.
Part B:
Add the following constraint to the problem:
2/3
7
+
≤
. Use the Geometric Method
to find the solution to the LP with the new constraint.
Part C:
Use the representation theorem to express the constraints in a different form.
Problem 2:
Look at the figure that follows and answer the set of questions based on the figure. The
feasible region is “striped”.
The feasible region is infinite.
The constraints are as
follows:
x
– 2 y
≤
4
x
–
y
≥
2
x
≥
0;
y
≥
0
Page 1 of 5
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View Full DocumentPart A:
List all corner points, if there are none, please write “none”
Part B:
Give an example of an objective function such that both (2,0) and (0,0) are optimal, but
(1,1) is not optimal (assume you are maximizing).
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 Spring '07
 JamesOrli
 Management, Optimization, LP, feasible region

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