practice_midterm1_3133(2)

# practice_midterm1_3133(2) - ISYE3133C Engineering...

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ISYE3133C - Engineering optimization Midterm 1 - February 20, 2008 NAME: GTID: SIGNATURE: Time: 50 minutes Instructions: WORK ALONE. Do not collaborate with anyone. Show ALL your work. You are NOT allowed to use any written notes or books. You are NOT allowed to use any electronic devices such as (but not limited to) calculators, PDAs, cell phones, laptops, etc. You will only receive credit for the work written on the exam itself or the extra pages I have provided. You will receive 2 extra credit points if you write a smiley face by your signature. 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. The Exam has 3 mandatory questions plus an optional extra credit questions. By signing above, you agree to abide by the letter and spirit of the GeorgiaTech Honor Code while taking this examination. Good luck!

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1. (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, jewel-encrusted 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 Jewel-encrusted 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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practice_midterm1_3133(2) - ISYE3133C Engineering...

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