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IEOR 4403 Adv Engineering & Corporate Economics
Professor Ali Sadighian
Fall 2011
Homework #4
Due in class on December 11th, 2011
Problem 1
a.
All linear programs must have (check all that
necessarily
apply):
1)
Objective function
2)
Dual variables
3)
Optimal solution
4)
Decision variables
5)
Constraints
6)
Active constraints
b.
Answer Yes or No (all questions below relate to linear programs):
1)
A feasible solution is defined as an assignment of decision variables such
that the objective function given by that assignment can be feasibly higher
or lower than the objective value given by other assignments.
2)
An optimal solution may not exist.
3)
The shadow price of an active constraint is zero.
4)
Simplex algorithm is a versatile computational method that solves linear
programs, integer programs and mixed integer programs.
5)
An optimal solution is not necessarily feasible because in some cases it
does not satisfy the definition from part (a) above.
6)
The following is NOT a linear program:
±² ³´
µ
¶ ·´
¸
¹º »º ¼½¾¿(À) ´
µ
¶ ³´
¸
Á ÂÃ
±ÄÅ½¾¿¼(À) Æ
Ç
È
´
µ
¶ ´
¸
Æ ÉÂ
c.
Answer
in
100 or less words (longer answers will be penalized).
In many decision environments the total number of major projects to be
considered is ten or fewer. Thus, enumeration of all combinations would be
feasible, since there would be 2
10
= 1,024 or fewer combinations. In such a case,
would it make sense to use a mathematical programming approach? What
information would the mathematical programming approach give that is not
available from enumeration?
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Problem 2
The Italian government is negotiating a restructure of its debt with its bond holders. In
order to convince the bond holders that this is a move of mutual benefit, the Italian
government has to prove that it has some good projects in hand and at the same time it
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