Determine whether the following statements about critical paths in networks are true:
There is only one critical path in every network.
The critical path is the shortest path in the network.
Activities on the critical path may have a non-zero float time.
The average duration of all paths on the network is equal to the duration of the critical path.
There may be multiple critical paths with the same duration through a network.
For each of the following networks:
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine the critical path through the network by listing the activities in order.
Find the duration of the critical path.
Given the following networks and activity tables:
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine the critical path through the network by listing the activities in order.
Find the duration of the critical path.
| Activity | Dependencies | Duration |
|---|---|---|
| A | - | 5 |
| B | A | 1 |
| C | A | 6 |
| D | A | 2 |
| E | B,C,D | 4 |
| F | E | 8 |
| Activity | Dependencies | Duration |
|---|---|---|
| A | - | 5 |
| B | - | 4 |
| C | - | 6 |
| D | A | 7 |
| E | B | 2 |
| F | D | 1 |
| G | C | 3 |
| H | G | 5 |
| I | E,F,H | 4 |
Find the float time of the given activity:
Given the following networks with the critical path highlighted in red:
List all non-critical activities.
List the non-critical activities in order and the float time of each activity.
Given the following networks:
Determine a critical path through the network by listing the activities in order.
List all non-critical activities.
List the non-critical activities in order and the float time of each activity.
Given the following networks:
List the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
List all non-critical activities.
List the non-critical activities in order and the float time of each activity.
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 | \text{Buy handtools.} | - | 2 |
| B | \text{Buy raw material.} | - | 4 |
| C | \text{Cut a hole in the wall.} | A | 3 |
| D | \text{Mix up cement.} | B | 2 |
| E | \text{Lay thin film of cement on the hole's borders.} | C, D | 3 |
| F | \text{Insert window frame.} | E | 1 |
| G | \text{Insert window.} | F | 1 |
| H | \text{Insert sealant and clean smudges.} | G | 2 |
Construct a network that correctly represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If the sealant arrived one hour after that activity's earliest start time, how would that affect the project finish time?
To bake a cake, several steps should be taken. The following activity table details these steps:
| Activity | Description | Dependencies | Duration (minutes) |
|---|---|---|---|
| A | \text{Look up recipe.} | - | 15 |
| B | \text{Buy ingredients.} | A | 30 |
| C | \text{Prepare cooking utensils.} | A | 10 |
| D | \text{Preheat oven.} | - | 5 |
| E | \text{Mix dry ingredients} \\ \text{(sugar, flour, baking powder, etc).} | B, C | 4 |
| F | \text{Mix wet ingredients} \\ \text{(eggs, milk, oil, etc).} | B, C | 6 |
| G | \text{Combine both mixtures.} | E, F | 3 |
| H | \text{Grease baking pan.} | B, C | 1 |
| I | \text{Pour mixture into baking pan.} | G, H | 2 |
| J | \text{Insert baking pan into oven.} | D, I | 30 |
Construct a network correctly that represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If you forgot to preheat the oven at the beginning and instead turned it on after you had poured the mixture into the pan, how would that affect the total time taken to bake the cake?
To manufacture a product, the following steps are to be taken:
| Activity | Description | Dependencies | Duration (days) |
|---|---|---|---|
| A | \text{Obtain workers.} | - | 7 |
| B | \text{Obtain raw materials.} | - | 4 |
| C | \text{Obtain design from engineers.} | - | 3 |
| D | \text{Train workers to use machines.} | A | 9 |
| E | \text{Produce part 1. } | B, C, D | 2 |
| F | \text{Produce part 2. } | B, C, D | 1 |
| G | \text{Produce part 3. } | B, C, D | 3 |
| H | \text{Test parts.} | E, F, G | 4 |
| I | \text{Assemble parts.} | H | 2 |
| J | \text{Test product.} | I | 3 |
| K | \text{Start mass production.} | J | 3 |
Construct a network that correctly represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If the production of Part 2 was delayed by 1 day, how would that affect the overall production time?
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:
| Activity | Description | Dependencies | Duration (minutes) |
|---|---|---|---|
| A | \text{Take order.} | - | 5 |
| B | \text{Relay order to kitchen.} | A | 2 |
| C | \text{Chef 1} \text{ cooks steak.} | B | 9 |
| D | \text{Chef 2} \text{ chops vegetables.} | B | 4 |
| E | \text{Chef 3} \text{ prepares the sauce.} | B | 4 |
| F | \text{Chef 2} \text{ finishes salad.} | D | 3 |
| G | \text{Chef 1} \text{ prepares the plate.} | C, E, F | 2 |
| H | \text{Waiter takes order to the table.} | G | 2 |
Construct a network correctly that represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If Chef 2 takes an extra minute chopping up the vegetables, how will that affect the time taken to prepare the meal?
The following table describes the steps involved in producing a movie:
| Activity | Description | Dependencies | Duration (days) |
|---|---|---|---|
| A | \text{Obtain script from writers.} | - | 5 |
| B | \text{Obtain equipment and set.} | - | 10 |
| C | \text{Cast and hire actors.} | A | 13 |
| D | \text{Hire employees.} | A, B | 9 |
| E | \text{Ready costumes and scenes.} | D | 20 |
| F | \text{Record scenes.} | C, E | 32 |
| G | \text{Edit recordings.} | F | 11 |
| H | \text{Combine scenes and finalise movie.} | G | 6 |
Construct a network that correctly represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If delivering the movie equipment took a few more days than planned, how would that affect the movie production time?
The following activity table describes the steps to build a dressing table:
| Activity | Description | Dependencies | Duration (days) |
|---|---|---|---|
| A | \text{Obtain wood, handles, junctions}\ldots | - | 7 |
| B | \text{Obtain mirror.} | - | 5 |
| C | \text{Obtain tools.} | - | 3 |
| D | \text{Build frame.} | A, C | 4 |
| E | \text{Build drawers.} | D | 2 |
| F | \text{Build top.} | D | 2 |
| G | \text{Fit top.} | F | 2 |
| H | \text{Fit drawers.} | E | 1 |
| I | \text{Sand surfaces then polish.} | G, H | 2 |
| J | \text{Insert drawer handles.} | I | 2 |
| K | \text{Insert mirror.} | B, I | 1 |
Construct a network that represents the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Find the critical path by listing the activities in order.
Find the duration of the critical path.
If the delivery of the mirror took an extra 5 days, how would that affect the project completion time?
To start a fire while camping, the following steps should be taken:
| Activity | Description | Dependencies | Duration (minutes) |
|---|---|---|---|
| A | \text{Gather logs, twigs, and dried leaves. } | - | 30 |
| B | \text{Obtain lighter or matches.} | - | 5 |
| C | \text{Pile up the dried leaves at the bottom.} | A | 7 |
| D | \text{Cover dried leaves with twigs.} | C | 3 |
| E | \text{Place two logs at the side of the pile} \\ \text{and one log across.} | D | 2 |
| F | \text{Light up the pile from the bottom. } | B, E | 2 |
Construct a network that correctly represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If finding a lighter or matches took 15 minutes longer, how would that affect the time taken to start the fire?
A company that produces padlocks takes the following steps in their manufacturing process:
| Activity | Description | Dependencies | Duration (minutes) |
|---|---|---|---|
| A | \text{Obtaining raw materials.} | - | 2 |
| B | \text{Bolt cutting.} | A | 3 |
| C | \text{Drilling and cutting the body.} | B | 6 |
| D | \text{Machining the barrel.} | B | 5 |
| E | \text{Pinning the barrel.} | D | 3 |
| F | \text{Groove cutting shackles.} | B | 1 |
| G | \text{Bending shackles.} | F | 1 |
| H | \text{Inserting shackle into body.} | C, E, G | 1 |
| I | \text{Inserting barrel into body.} | H | 2 |
| J | \text{Testing key set.} | I | 1 |
| K | \text{Packaging} | J | 3 |
Construct a network that correctly represents the information in the activity table.
Construct a table by listing all the vertices, the earliest starting time (EST) and latest starting time (LST) for each vertex.
Determine a critical path through the network by listing the activities in order.
Find the duration of the critical path.
If the machine that pins the barrel broke down and took 2 minutes to repair before being operational, how would that affect the time taken to produce a padlock?