Department of Agricultural and Resource Economics
“We are what we repeatedly do.
Excellence then is not an act, but a habit.”
Aristotle
Copyright c
±
2010 by Quirino Paris.
ARE 155
Winter 2010
Prof. Quirino Paris
HOMEWORK #2
Due Tuesday, January 19
1.
Given the following LP problem
max
Z
= 6
x
1
+ 3
x
2
subject to
2
x
1
+ 6
x
2
≤
12
5
x
1
+ 2
x
2
≤
10
x
1
and
x
2
≥
0
a) Graph the output space.
b) Graph the input requirement space (do not forget vectors associated with slack
variables).
c) For each extreme point (basic feasible solution) in the output space indicate
the corresponding basis in the input requirement space.
d) Solve the problem by graphical methods and report the optimal basis and the
optimal solution. (In a graph, it may be diﬃcult to read the exact optimal solution.
Be as accurate as possible: choose the appropriate measurement units on the axes of
your diagram.)
2.
Given the following LP problem
max
TR
= 2
x
1
+ 4
x
2
+ 6
x
3
subject to
3
x
1
+
x
2
−
4
x
3
≤
9
−
x
1
+ 4
x
2
+ 3
x
3
≤
8
x
i
≥
0
, i
= 1
,
2
,
3
a) graph the set of constraints in the input requirement space and indicate ex
plicitly all the feasible bases.
b) for each feasible basis in a) write down the corresponding basic feasible solution
in
qualitative terms
.
c) Use the notion of a total cost function to derive marginal cost. Derive marginal
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 Winter '08
 Staff
 Linear Programming, Optimization, Dual problem, max T

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