University of California, Davis
Department of Agricultural and Resource Economics
“We are what we repeatedly do.
Excellence then is not an act, but a habit.”
Aristotle
Copyright c 2011 by Quirino Paris.
ARE 155
Winter 2011
Prof. Quirino Paris
HOMEWORK #3
Due Tuesday, January 25
1.
Given the following primal LP problem
min
TC
= 3
x
1
+ 4
x
2
subject to
3
x
1
+ 2
x
2
≥
6
2
x
1
−
x
2
≤
8
x
i
≥
0
, i
= 1
,
2
a) Graph the primal problem. Write down all the extreme points and the associ
ated primal feasible bases.
b) Write down the dual problem (Be careful to have all the inequalities going in
the right direction before writing the dual.)
c) Graph the dual problem. Write down all the extreme points of the dual problem
and the associated dual feasible bases.
d) Verify graphically that the basis
"
2
−
1
1
0
#
in the primal problem is not a feasible basis.
2. An investor wants to allocate her inheritance income among four construction
projects and annual certificates of deposit.
The outlays and cash inflows of each
construction project for the first three years are as follows:
Beginning of year
Project
First
Second
Third
I
−
1
,
000
+200
+300
II
−
1
,
200
−
300
+200
III
−
900
−
100
−
150
IV
−
1
,
100
−
100
−
200
1
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(A minus sign indicates a cash outlay, while a plus sign indicates a cash inflow.)
After the third year, the information about the profitability of each project is
summarized in its net present value (at the beginning of the fourth year) as follows:
Project I, $250; project II, $300; project III, $360; project IV, $420.
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 Spring '08
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 Optimization, Dual problem, Superintendent

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