OEM Class of 2009
DMOR Homework #3: Due Saturday, October 6
th
at the start of class.
Question 1.
Consider the following set of equations.
x
1
+
x
2
–
x
3
= 1
x
1
+ 2
x
2
= 3
2
x
2
+
x
3
+
x
4
= 3
Part a:
Calculate all extreme points of the feasible region given by those constraints,
along with the restrictions that
x
≥ 0.
Do this by choosing every possible set of basic
variables and solving three equations in three unknowns (not by graphing).
Part b:
Let
x
1
,
x
2
, and
x
3
be basic, and solve for those variables in terms of the nonbasic
variable
x
4
.
Now, suppose that you want to increase
x
4
.
How large can
x
4
become before
either
x
1
,
x
2
, or
x
3
becomes negative?
Part c:
Take
x
4
equal to the largest value allowed in part b, and adjust the values of
x
1
,
x
2
,
and
x
3
accordingly (using the fact that you’ve already solved for those basic variables in
terms of
x
4
).
Verify that this new solution corresponds to another one of the basic
feasible solutions found in part a.
Question 2.
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 Fall '09
 VLADIMIRLBOGINSKI
 Optimization, basic variables

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