Before a new product can be introduced, the activities in Table must be completed (all times are in weeks).
Activity
|
Description
|
Predecessors
|
Duration
|
a
|
b
|
m
|
A
|
Design the product
|
—
|
6
|
2
|
10
|
6
|
B
|
Survey the market
|
—
|
5
|
4
|
6
|
5
|
C
|
Place orders for raw materials
|
A
|
3
|
2
|
4
|
3
|
D
|
Receive raw materials
|
C
|
2
|
1
|
3
|
2
|
E
|
Build prototype of product
|
A, D
|
3
|
1
|
5
|
3
|
F
|
Develop ad campaign
|
B
|
2
|
3
|
5
|
4
|
G
|
Set up plan for mass production
|
E
|
4
|
2
|
6
|
4
|
H
|
Deliver product to stores
|
G, F
|
2
|
0
|
4
|
2
|
a Draw the project diagram.
b Determine all critical paths and critical activities.
c Determine the total float and free float for each activity.
d Set up an LP that can be used to determine the critical path.
e Formulate an MCNFP that can be used to find the critical path.
f It is now 12 weeks before Christmas. What is the probability that the product will be in the stores before Christmas?
g The duration of each activity can be reduced by up to 2 weeks at the following cost per week: A, $80; B, $60; C, $30; D, $60; E, $40; F, $30; G, $20. Assuming that the duration of each activity is known with certainty, formulate an LP that will minimize the cost of getting the product into the stores by Christmas.