2. [25] Suppose you are assigned to manage the house-building project, whose details are
shown in the following table.
Activity
A
B
C
D
E
F
G
Description
Build foundation
Build walls and ceilings
Build the roof
Electrical wiring
Install windows
Put on siding
Painting
Predecessor
S
A
B
C
D
E
F
G
Cost per day of
Activity reducing the activity
duration
A
B
B
B
E
C,F
a) Draw the project diagram, and find the critical path, total duration, and total float
and free float for every activity.
$30k
$15k
$20k
$40k
$20k
$30k
$40k
b) Suppose you are expected to finish the project within 20 days. You find you have to
hire more workers in order to shorten the total duration. Please find the minimum
cost to achieve the goal. The cost table is shown as follows,
Maximum
possible
reduction in
activity
duration
Duration(days)
5
8
10
5
2
3
1
2
4
6
3
2
3
1
You can use any method to solve the linear program, e.g., graphical, simplex, excel,
mpl, etc., except copying.