Question

A construction project consists of four activities. The quantity of work, manpower requirement, and the productivity of the activities are listed in the table below. The interrelationship between the activities are also mentioned in the table. The construction project will start on January 29. Assume no holidays for the entire duration of the project. The project will finish on February \underline{\hspace{1cm}} [mention date in number].\[\begin{array}{|c|c|c|c|c|} \hline Activity & Quantity (cu.m) & Manpower (persons) & Productivity (cu.m/man-day) & Immediate Successor Activity \\ \hline \text{A} & \text{96} & \text{8} & \text{3} & \text{C} \\ \hline \text{B} & \text{252} & \text{7} & \text{4} & \text{C \} & \text{D} \\ \hline \text{C} & \text{275} & \text{5} & \text{5} & \text{Nil} \\ \hline \text{D} & \text{126} & \text{6} & \text{3} & \text{Nil} \\ \hline \end{array}\]

Hint:

Critical path = Longest dependency chain. Always compute durations with manpower × productivity, then track dependencies.

Answer 1

Step 1: Calculate duration of each activity.
Formula: \[ \text{Duration} = \frac{\text{Quantity}}{\text{Manpower} \times \text{Productivity}} \] - Activity A: \( \frac{96}{8 \times 3} = \frac{96}{24} = 4 \; \text{days} \)
- Activity B: \( \frac{252}{7 \times 4} = \frac{252}{28} = 9 \; \text{days} \)
- Activity C: \( \frac{275}{5 \times 5} = \frac{275}{25} = 11 \; \text{days} \)
- Activity D: \( \frac{126}{6 \times 3} = \frac{126}{18} = 7 \; \text{days} \)

Step 2: Dependencies.
- A → C
- B → C \& D
So: - C can start only after both A and B are completed. - D can start only after B is completed.

Step 3: Timeline.
- Start date = Jan 29. - A: 4 days → finishes Feb 1. - B: 9 days → finishes Feb 6. - C: Starts after A and B = Feb 6, runs 11 days → finishes Feb 16. - D: Starts after B = Feb 6, runs 7 days → finishes Feb 12.

Step 4: Project completion.
Since the project finishes when the last activity (C or D) finishes, completion = Feb 16.

Final Answer: \[ \boxed{\text{February 16}} \]