Question

Assume the network and data that follow:

Activity	Normal Time(Weeks)	Normal Cost	Crash Time(weeks)	Crash cost	Immediate Processors
A	2	\(50	1	\)70	-
B	4	80	2	160	A
C	8	70	4	110	A
D	6	60	5	80	A
E	7	100	6	130	B
F	4	40	3	100	D
G	5	100	4	150	C,E,F

a. Construct the network diagram.

b. Indicate the critical path when normal activity times are used.

c. Compute the minimum total direct cost for each project duration based on the cost associated with each activity. Consider the duration of 13, 14, 15, 16, 17, and 18 weeks.

d. If the indirect costs for each project duration are \(400 (18 weeks), \)350 (17 weeks), \(300 (16 weeks), \)250 (15 weeks), \(200 (14 weeks), and \)150 (13 weeks), what is the total project cost for each duration? Indicate the minimum total project cost duration.

Short answer

The critical path is the longest path of the network diagram. It represents the minimum time required to complete the entire process.

Step-by-step solution

(a) Network Diagram

Anetwork diagram is a kind of visual representation that is used to analyze the whole activities that needed to be completed at a particular given time.

(b) The critical path when normal activity is used

The critical pathis a method that is used to identify the necessary tasks that are needed to be completed in the given time interval.

In this case, the critical pathis A-B-E-G. This critical path consists of zero slack. Any delays in these activities will delay the entire process.

(c) Calculate the total direct cost

Direct costsare the cost that the business incurs directly in the production of goods and services.

Those numbers that are written in bold are the direct costs.

(d) Total project cost

The cost that is involved in the production of any particular project assigned to the business is said to be the project cost.