| Course | BU 442 Cost and Time Management |
|---|---|
| Unit | Unit 4 |
| Paper type | Network diagram and critical path |
| Length | About 740 words, 5 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Project Management |
| Updated | September 2026 |
Free sample paper for BU 442 Unit 4
Two Critical Paths Through the Walls and 135 Working Days: A Network Diagram and Critical Path Analysis for an Invented Nonprofit's Shared Kitchen in Indiana
Student Name
Business, Herzing University
BU 442: Cost and Time Management
Instructor Name
February 25, 2026
Two Critical Paths Through the Walls and 135 Working Days: A Network Diagram and Critical Path Analysis for an Invented Nonprofit's Shared Kitchen in Indiana
Purpose and Conventions
This network links the sixteen work packages defined for Fort Wayne Food Works, an invented nonprofit building a shared commercial kitchen in a former Fort Wayne hardware store, to find what actually drives the finish date. It justifies every dependency, runs the forward and backward passes, reports total and free float for each package and names the path that has none. The critical path method dates from Kelley and Walker (1959), who showed that the longest chain of dependent activities fixes a project's shortest possible duration and that activities off that chain can slip without delaying the finish.
Conventions: durations are in working days; all dependencies are finish-to-start with no lag unless stated; day 0 is the project start, planned for Monday, February 2, 2026; an activity's early start is the latest early finish among its predecessors. The diagram, drawn as activity-on-node boxes, cannot be reproduced here, so its content appears in the tables.
The Dependencies and Why Each Exists
A dependency is drawn only where one package physically or legally cannot start before another finishes. Each is justified below.
| Package | Duration | Depends on | Reason |
|---|---|---|---|
| 1.1 Design | 30 | Start | Nothing precedes it |
| 1.2 Permit review | 20 | 1.1 | The city reviews finished permit drawings |
| 2.1 Demolition and abatement | 10 | 1.1 | Demolition scope comes from the design; a separate demolition permit allows it before the building permit |
| 4.1 Hood fabrication | 30 | 1.1 | The fabricator needs the design's hood schedule |
| 4.3 Walk-in fabrication | 25 | 1.1 | The vendor needs the design's box sizes |
| 3.1 Electrical service | 25 | 1.2, 2.1 | Needs the building permit and a cleared building |
| 3.2 Plumbing and interceptor | 20 | 1.2, 2.1 | Same |
| 3.3 Mechanical systems | 20 | 1.2, 2.1 | Same |
| 5.1 Interior construction | 25 | 3.2, 3.3 | Pipes and ducts inside walls and ceilings must be in before they are closed; new circuits run in surface conduit, so electrical work does not hold the walls |
| 4.2 Hood installation | 5 | 4.1, 5.1 | Hoods must be delivered, and wall panels behind them finished |
| 4.4 Walk-in installation | 15 | 4.3, 5.1 | Panels delivered and the floor under them finished |
| 3.4 Fire suppression | 8 | 4.2 | Suppression mounts on the installed hoods |
| 4.5 Equipment setting | 10 | 3.1, 4.2, 4.4 | Equipment needs power, sits under hoods and beside the walk-ins |
| 6.1 Inspections and approval | 10 | 3.4, 4.5 | Inspectors test complete systems |
| 6.2 Commissioning and training | 5 | 6.1 | Tenants train only in an approved kitchen |
Forward and Backward Passes
The forward pass sets each package's early start and finish, beginning at day 0. Design runs from 0 to 30. Permit review, demolition, hood fabrication and walk-in fabrication all start at day 30; they finish at days 50, 40, 60 and 55. Electrical, plumbing and mechanical work start at day 50, the later of the permit and demolition finishes, and finish at 75, 70 and 70. Interior construction starts at 70 and finishes at 95. Hood installation starts at 95, the later of its two predecessors, and finishes at 100; walk-in installation starts at 95 and finishes at 110. Fire suppression runs from 100 to 108. Equipment setting waits for the latest of its three predecessors, the walk-ins at day 110, and finishes at 120. Inspections run from 120 to 130, and commissioning from 130 to 135.
The backward pass starts from day 135 and works back, setting each package's late finish as the earliest late start among its successors. The results are in the table. Total float is each package's late start minus its early start, the measure the PMBOK guide uses to identify the critical path as the sequence with the least float (Project Management Institute, 2017).
| Package | ES (day) | EF (day) | LS (day) | LF (day) | Total float | Free float |
|---|---|---|---|---|---|---|
| 1.1 Design | 0 | 30 | 0 | 30 | 0 | 0 |
| 1.2 Permit review | 30 | 50 | 30 | 50 | 0 | 0 |
| 2.1 Demolition | 30 | 40 | 40 | 50 | 10 | 10 |
| 4.1 Hood fabrication | 30 | 60 | 75 | 105 | 45 | 35 |
| 4.3 Walk-in fabrication | 30 | 55 | 70 | 95 | 40 | 40 |
| 3.1 Electrical | 50 | 75 | 85 | 110 | 35 | 35 |
| 3.2 Plumbing | 50 | 70 | 50 | 70 | 0 | 0 |
| 3.3 Mechanical | 50 | 70 | 50 | 70 | 0 | 0 |
| 5.1 Interior | 70 | 95 | 70 | 95 | 0 | 0 |
| 4.2 Hood installation | 95 | 100 | 105 | 110 | 10 | 0 |
| 4.4 Walk-in installation | 95 | 110 | 95 | 110 | 0 | 0 |
| 3.4 Fire suppression | 100 | 108 | 112 | 120 | 12 | 12 |
| 4.5 Equipment setting | 110 | 120 | 110 | 120 | 0 | 0 |
| 6.1 Inspections | 120 | 130 | 120 | 130 | 0 | 0 |
| 6.2 Commissioning | 130 | 135 | 130 | 135 | 0 | 0 |
The Paths With No Float
Two paths have zero total float and share every package except one: design, permit review, then either plumbing or mechanical work, then interior construction, walk-in installation, equipment setting, inspections and commissioning. Both run 135 working days. Because plumbing and mechanical work are the same length and both feed the interior, a slip in either delays the finish, and accelerating only one of them gains nothing. That is the practical meaning of two critical paths: recovery must address both at once.
The finish at day 135 falls in mid-August 2026, after the Memorial Day and Independence Day holidays are added to the calendar.
What the Float Figures Say
Total float is how long a package can slip without delaying the project; free float is how long it can slip without delaying any successor. The difference matters in two places. Hood installation has ten days of total float but no free float: any slip delays fire suppression, even though the project finish is safe for ten days. A manager watching only total float would not warn the suppression contractor. Electrical service has 35 days of both, which looks comfortable, but its float disappears if the utility requires a new transformer, the pessimistic case in the estimate; a delay of that size would make electrical critical through equipment setting.
The largest floats belong to the fabrication packages, 45 days for hoods and 40 for walk-ins. That float exists only because fabrication starts as soon as design is finished. If the board delays orders until the permit is issued to protect cash, hood fabrication would start at day 50 and its float would fall to 25 days. Kerzner (2017) warns that float belongs to the project, not to the activity that happens to hold it, and the Food Works plan records that ordering the hoods and walk-ins early is what keeps them off the critical path. Every duration and date here belongs to the composite case for this course.
References
Kelley, J. E., & Walker, M. R. (1959). Critical-path planning and scheduling. In Papers presented at the December 1-3, 1959, Eastern Joint IRE-AIEE-ACM Computer Conference (pp. 160-173). Association for Computing Machinery. https://doi.org/10.1145/1460299.1460318
Kerzner, H. (2017). Project management: A systems approach to planning, scheduling, and controlling (12th ed.). Wiley.
Project Management Institute. (2017). A guide to the project management body of knowledge (PMBOK guide) (6th ed.). Project Management Institute.
What the BU 442 Unit 4 instructions ask for
The fourth unit of BU 442 asks students to build a project network, calculate the schedule and identify the critical path. Typical requirements include a network diagram, justified dependencies, a forward and backward pass, early and late dates, total and free float for each activity, and identification of the critical path. Many instructors accept a diagram drawn with software or by hand, or its content in tables. Students are often asked what happens when more than one path has zero float. Explanations of float should be practical, telling a manager what can slip and who needs a warning. The deliverable is usually tables and a narrative in APA 7, and strong submissions explain what the float figures mean for managing the work.
How the BU 442 Unit 4 example is put together
The paper sets out conventions, including day numbering and dependency types. A dependency table gives each package's duration, predecessors and the reason for each link, and explains why electrical work does not hold the walls. The forward pass is narrated package by package, and the backward pass results appear in a table of early and late dates with total and free float. A section identifies the two zero-float paths and explains why both must be recovered together. The final section interprets float, contrasting total and free float for hood installation, noting how electrical float could vanish and showing that fabrication float depends on ordering before the permit.
BU 442 Unit 4 rubric: what full points look like
Herzing instructors usually grade network units on dependency logic, calculation accuracy, float analysis, critical path identification and interpretation, with presentation and sources. Dependency logic earns full credit when each link has a stated reason. Calculation accuracy is judged on correct forward and backward passes, since one error propagates. Float analysis scores highest when both total and free float are calculated and the difference between them is explained. Critical path identification rewards noticing multiple zero-float paths. Interpretation earns points when the student explains what float means for decisions, such as which contractors to warn or which orders to place early, rather than only reporting the numbers. Tables that let the instructor check each figure are strongly preferred.
Common BU 442 Unit 4 mistakes, and how to avoid them
Network analyses commonly lose points by drawing dependencies without justification, which can create false critical paths. Another frequent error is miscalculating the backward pass at merge points, where the earliest late start among successors must be used. Students often report only total float and miss free float, which tells a manager whether a slip affects the next activity. Some identify one critical path and overlook a second of equal length. Others treat float as belonging to the activity rather than the project. Diagrams without tables make checking hard. Finally, ignoring the calendar when converting days to dates can put a finish date on a holiday, which a sponsor will notice before the student does.
Get a BU 442 Unit 4 example written to your instructions
We work from the Unit 4 instructions, the BU 442 rubric in your classroom, the breakdown and durations the assignment builds on, and any software your section requires. We write a custom example that registers each dependency with a reason, shows both passes in full, separates the two floats and closes on the near-critical chains. First custom sample free, returned in 24 to 48 hours.
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- BU 442 Unit 6: Earned value calculation
- BU 442 Unit 7: Variance analysis with response
- BU 442 Unit 8: Forecast and status report
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- BU 345 Unit 4: Schedule and dependency chart
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BU 442 Unit 4 questions, answered
Does the diagram have to be drawn by hand?
Check the instructions, since some sections want the network drawn and others accept output from scheduling software. Where a tool produces the dates, show the calculation for at least one chain anyway, because a printout proves the software ran and not that you can compute float. Where you draw it yourself, keep the node layout readable rather than compressing everything onto one line.
What if more than one path has zero float?
Then the project has two critical paths and saying so is the right answer rather than a problem to hide. Report both, note that either one slipping moves the finish, and point out that the schedule is more fragile than a single path would be. Assignments often build this in deliberately, and drafts that pick one chain and ignore the other lose the observation.
How much explanation do the dependencies need?
A line each is usually enough, and the line has to say why rather than what. Recording that testing follows build states the arrow again; recording that testing needs a working version to run against explains it. Where a relationship exists only because of how you chose to staff the work, say so, since those are the ones that can be renegotiated when the finish date gets tight.
Where can I find a free BU 442 Unit 4 sample paper?
A complete BU 442 Unit 4 network diagram and critical path example is free above, with the dependency table, both passes and margin notes. For your own project's network, we will work one out from your prompt without charge, generally within 48 hours.
What if two paths have zero float in BU 442 Unit 4?
Both are critical, and recovery must address both. In the sample, plumbing and mechanical work are equal in length and both feed the interior, so speeding up only one would not change the finish date.