Exam - IOE 310 Winter 2007 Final Exam Name Instructions...

IOE 310 Winter 2007
Final Exam
April 13, 2007
Name:
Instructions
• This is a closed book, closed notes exam.
• You may use one double sided 8 × 11 inch note sheet and calculator during the exam.
Note that not all problems carry the same weight.
• There are 5 problems in the exam and 12 pages (including this one). You can use
the back of each sheet for rough calculations.
• Please write your solutions to each problem in the space provided. Show all work and
write legibly. Your grade will depend in part on the completeness and clarity of your
answers.
• Sign your name below after reading the Honor Pledge. Instructors are not required to
grade exams in which the Honor Pledge is not signed.
Good luck!
Honor Pledge: “I have neither given nor received aid on this examination.”
Signed:
1

Problem 1 (10 points)
For each of the following statements, determine whether it is true or false and explain why.
a) The total float of an activity in a project is f . Then this means the activity can be delayed
by f time units without delaying any of the successors of that activity.
Answer: T/F Reason:
b) Suppose we have a transportation problem with the following objective function:
min z =
i ∈ S j ∈ D
c
ij
x
ij
Then the following is the correct AMPL structure for the objective function:
minimize z { i in S } : sum { j in D } c[i,j]*x[i,j];
Answer: T/F Reason:
c) Suppose we are solving an integer program using branch and bound. As we branch further
down the tree, the objective function at each of the nodes can only increase.
Answer: T/F Reason:
2

d) Consider the following problems:
(1) min c
T
x (2) max b
T
y
s.t. s.t.
Ax ≥ b A
T
y ≤ c
x ≥ 0 y ≥ 0
Assume ¯ x and ¯ y are feasible solutions to problems (1) and (2) respectively. Then by the
weak duality theorem:
c
T
¯ x ≤ b
T
¯ y
Answer: T/F Reason:
Write your explanations for the following question.