```
gantt
    dateFormat  DD-MM-YYYY
    title Revised Project Schedule (Late Start)

    %% Milestones
    section Milestones
    Prototype Delivery Milestone        :milestone, m1, 01-03-2024, 0d
    Intermediate Modules Milestone      :milestone, m2, 01-06-2024, 0d
    Project Completion Milestone        :milestone, m3, 01-09-2024, 0d

    section Analysis
    a :a, 01-01-2024, 18d
    b :b, after a, 20d
    c :c, after b, 22d
    milestonec :milestone, m1, after c, 0d

    section Design
    d :d, after b, 25d
    e :e, after d, 15d
    f :f, after d, 25d
    g :g, after f, 15d
    h :h, after d, 15d
    i :i, after d, 20d
    j :j, after f and g, 12d
    k :k, after j, 12d

    section Implementation
    l :l, after k, 30d
    m :m, after e, 20d
    n :n, after f, 20d
    o :o, after h, 12d
    p :p, after i and g,25d
    q :q, after i,30d
    r :r, after n,25d
    s :s, after n,25d
    t :t, after l and m and p and q and r and s, 20d
    milestonei :milestone, m2, after t, 0d

    section Deployment
    u :u, after t and o, 5d
    v :v, after u,5d
    w :w, after v,5d
    x :x, after w,12d
    y :y, after x,20d
    z :z, after y,20d
    milestonef :milestone, m3, after z, 0d
```

### Forward Pass (Calculating Early Start and Early Finish)

| Task | Duration (Days) | Predecessors      | Early Start (ES) | Early Finish (EF) |
|------|-----------------|-------------------|-------------------|-------------------|
| a    | 18              | -                 | 0                 | 18                |
| b    | 20              | a                 | 18                | 38                |
| c    | 22              | b                 | 38                | 60                |
| d    | 25              | b                 | 38                | 63                |
| e    | 15              | d                 | 63                | 78                |
| f    | 25              | d                 | 63                | 88                |
| g    | 15              | f                 | 88                | 103               |
| h    | 15              | d                 | 63                | 78                |
| i    | 20              | d                 | 63                | 83                |
| j    | 12              | f, g              | 103               | 115               |
| k    | 12              | j                 | 115               | 127               |
| l    | 30              | k                 | 127               | 157               |
| m    | 20              | e                 | 78                | 98                |
| n    | 20              | f                 | 88                | 108               |
| o    | 12              | h                 | 78                | 90                |
| p    | 25              | i, g              | 103               | 128               |
| q    | 30              | i                 | 83                | 113               |
| r    | 25              | n                 | 108               | 133               |
| s    | 25              | n                 | 108               | 133               |
| t    | 20              | l, m, p, q, r, s  | 157               | 177               |
| u    | 5               | t, o              | 177               | 182               |
| v    | 5               | u                 | 182               | 187               |
| w    | 5               | v                 | 187               | 192               |
| x    | 12              | w                 | 192               | 204               |
| y    | 20              | x                 | 204               | 224               |
| z    | 20              | y                 | 224               | 244               |

### Backward Pass (Calculating Late Start and Late Finish)

Assuming the project's finish time is 244 days.

Here's the completed backward pass table:


| Task | Duration | Successors          | Late Start (LS) | Late Finish (LF) | Slack (LS - ES) |
|------|----------|---------------------|-----------------|------------------|-----------------|
| z    | 20       | -                   | 224             | 244              | 0               |