ISYE3133C  Engineering optimization
Midterm 1  February 20, 2008
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Time: 50 minutes
Instructions:
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WORK ALONE.
Do not collaborate with anyone.
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Show ALL your work.
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You are NOT allowed to use any written notes or books.
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You are NOT allowed to use any electronic devices such as (but not limited to) calculators, PDAs,
cell phones, laptops, etc.
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You will only receive credit for the work written on the exam itself or the extra pages I have
provided.
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You will receive 2 extra credit points if you write a smiley face by your signature.
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You will ﬁnd the dual of a normal max problem at the end of the exam. You can use this in any
of the question.
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The Exam has 3 mandatory questions plus an optional extra credit questions.
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By signing above, you agree to abide by the letter and spirit of the GeorgiaTech Honor Code while
taking this examination.
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Good luck!
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View Full Document1.
(4 pts each for a total of 20 pts)
For each of these statements, mark True or False (no
justification needed):
a) F  Every maximization LP with an unbounded feasible region has solutions with an
arbitrarily large objective value.
b) F  A linear programming problem must have an integer optimal solution.
c) F  For a primal/dual pair of linear problems, the primal problem is unbounded if and
only if the dual problem is infeasible.
d) T  The dual of the dual is the primal.
e) T  If there are infinitely many optimal solutions for a linear program, then at least one
must be an extreme point of the feasible region.
2. (50 pts Total) Pirate Treasure
Long John Silver the pirate discovered a vast treasure hidden on a deserted island.
There
were limitless amounts of gold and silver coins, jewelencrusted plates, and ivory statues,
all of which were completely unguarded and could be taken at no risk.
Unfortunately,
Long John’s ship had been sunk, and he had only a small rowboat in which to put his
treasure.
The rowboat could hold up to 700 pounds (plus the pirate himself) and a
volume of 700 cubic feet.
The table below gives the value, size, and weight of each type of treasure (nevermind the
weird sizes, values and weights):
Value
(thousands of
dollars)
Size (cubic feet)
Weight (pounds)
Gold coin
2
4
4
Silver coin
1
1
2
Jewelencrusted
plate
4
2
1
Ivory statue
15
3
5
Being a very worldly and intelligent pirate, Long John was familiar with the basic
principles of linear programming, and set up the following LP to help him decide how
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 Spring '08
 JuanPabloVielma
 Linear Programming, Optimization, optimal solution, John Silver, Long John

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