NZ Level 8 (NZC) Level 3 (NCEA) [In development] Applications of Critical Paths

## Interactive practice questions

In order to insert a window, several activities need to be performed to complete the project. The following table displays the project’s activities and their descriptions, dependencies, and durations.

Activity Description Dependencies Duration (hours)
$A$A Buy handtools - $2$2
$B$B Buy raw material - $4$4
$C$C Cut a hole in the wall $A$A $3$3
$D$D Mix up cement $B$B $2$2
$E$E Lay thin film of cement on the hole's borders. $C,D$C,D $3$3
$F$F Insert window frame $E$E $1$1
$G$G Insert window $F$F $1$1
$H$H Insert sealant and clean smudges. $G$G $2$2
a

Which network correctly represents the information in the activity table? A B C D A B C D
b

Find the earliest starting time (EST) for each vertex.

Vertex Start 1 2 3 4 5 6 Finish
EST $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
c

Now find the latest starting time (LST) for each vertex.

Vertex Start 1 2 3 4 5 6 Finish
EST $0$0 $2$2 $4$4 $6$6 $9$9 $10$10 $11$11 $13$13
LST $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
d

Determine a critical path through the network by listing the activities in order.

Write all activities on the same line, separated by commas

e

What is the duration of the critical path?

f

If the sealant arrived one hour after that activity's earliest start time, how would that affect the project finish time?

There would be no effect on the finish time for the project.

A

The project would be delayed by one hour.

B

The project would finish one hour earlier.

C

There would be no effect on the finish time for the project.

A

The project would be delayed by one hour.

B

The project would finish one hour earlier.

C
Easy
Approx 5 minutes

To bake a cake, several steps should be taken. The following activity table details these steps.

To manufacture a product, the following steps are to be taken.

At a restaurant, taking the order of and preparing a steak with mushroom sauce and a side of salad goes through several stages before reaching the customer. The following table describes these stages:

### Outcomes

#### M8-5

Develop network diagrams to find optimal solutions, including critical paths.

#### 91576

Use critical path analysis in solving problems