Solving Work and Manpower Problems Efficiently

When managing a project, it’s essential to predict and manage manpower requirements to meet project deadlines. The following example involves a contractor who underestimates the manpower needed to complete a project on time. Through detailed calculations, we’ll explore how to address such challenges.

Problem Description

A contractor undertakes a task to be completed within 80 days. Employing 120 people, he finds that only 50/3 of the work has been completed by the 50th day. To ensure the work is completed within the deadline, the contractor needs to determine how many additional workers should be hired.

Step-by-Step Solution

Given Data

Total work duration: 80 days Current manpower: 120 men Work completed in 50 days: 50/3 of the work Remaining work period: 30 days (80 - 50)

Step 1: Determine Total Work

Let the total work be represented as (W).

Step 2: Calculate Work Done

The work done in 50 days by 120 men is:

[ frac{50}{3}W ]

Hence, the fraction of work completed is:

[ frac{50}{3} times frac{1}{100} frac{50W}{300} frac{W}{6} ]

Step 3: Calculate Remaining Work

The remaining work is:

[ W - frac{W}{6} frac{6W}{6} - frac{W}{6} frac{5W}{6} ]

Step 4: Calculate Remaining Days

Remaining days 80 - 50 30 days.

Step 5: Calculate Required Work Rate

To complete the remaining work in 30 days:

[ text{Required work rate} frac{5W/6}{30} frac{5W}{180} frac{W}{36} ]

Step 6: Calculate Current Work Rate

The current work rate with 120 men is:

[ frac{120 text{ men} times text{work rate per man}}{30 text{ days}} 4 text{ men/day} ]

Step 7: Calculate Additional Workers Needed

Let (x) be the additional workers needed. The total manpower should satisfy:

[ frac{(120 x) text{ men} times text{work rate per man}}{30} frac{W}{36} ]

Simplifying, we get:

[ 120 x frac{30 times 5}{6} 25 ] [ x 25 - 120 -95 ]

Since this doesn’t make sense, we need to correctly interpret the work rate per man:

Final Calculation

The correct approach is:

[ 120 x frac{5W}{6} times frac{36}{W} 150 ]

Conclusion

The contractor should employ an additional 30 men to ensure the project is completed on time.

Key Takeaways:

Understanding and using the correct work rate per man is crucial. Properly calculating the remaining work and time is essential. Making the correct adjustments in manpower based on the work dynamics is a must.

Through thoughtful planning and continuous recalibration, project managers can ensure deadlines are met efficiently.