PROJECT MANAGEMENT
SUMMER 2014 HOMEWORK 1
1. Consider the seven projects below. The cash required for each project and its net present value
(NPV) each investment adds to the firm are listed in the table below. The cash available for
investment is $15K. Partial investments in a particular project are not allowed.
(a) Formulate the model that finds the set of projects that maximizes NPV and requires that
project 2 must be selected if project 1 is selected.
(b) Formulate the model that finds the set of projects that maximizes NPV and requires either
project 1 or project 3 (or both) to be selected.
Project
1
2
3
4
5
6
7 Cash Required
$5K
$2.5K
$3.5K
$6K
$7K
$4.5K
$3K NPV
$16K
$8K
$10K
$20K
$22K
$12K
$8K 2. Consider the project below with 15 activities. For each activity, the immediate predecessors(s),
immediate succesors(s), and duration (in days) are given. Assume that activity A can begin
immediately and activity O is the last activity to be completed. Show the AON network for this
project. Also, find the time to complete the project and the activities that are on the critical path.
Task
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O Immediate
Predecessor(s)
None
A
B
B
C
D, E
C, D
F
F
G
I
H, K
J, L
L
M, N Immediate
Successor(s)
B
C, D
E, G
F, G
F
H, I
J
L
K
M
L
M, N
O
O
None 3. Show the AOA network that depicts the following precedence constraints:
(a) Task A precedes Task D
(b) Tasks A and B precede Task E
(c) Tasks B and C precede Task F
You can ignore the Start and End project milestones. Duration
10
6
6
12
4
3
6
12
3
14
4
3
8
12
4
