Question

A project was expected to be completed in 11 weeks by a crew of six (6) workers. The work was to be completed without overtime, namely, with 40-hour workweeks. Workers were to be paid $20 per hour, which included all fringes. Before construction began, the owner decided that the project schedule was to be accelerated by having the workers work 8 hours on Saturdays. Assume wages are paid at time-and-a-half on Saturdays - What is the revised expected duration of the project? - What is the added cost due to the acceleration?

Answer 1

≈$13,315.20

Step-by-step explanation:

Before the acceleration, the crew of 6 workers worked 40 hours per week, for a total of:

6 workers × 40 hours/worker/week = 240 hours/week

The project was expected to take 11 weeks, for a total of:

11 weeks × 240 hours/week = 2,640 hours

The cost of labor for the original schedule would be:

240 hours/week × $20/hour/worker × 6 workers = $28,800/week

Over 11 weeks, this would be a total labor cost of:

$28,800/week × 11 weeks = $316,800

Now, with the accelerated schedule, the workers will work an extra 8 hours on Saturdays, for a total of:

6 workers × 8 hours/worker = 48 hours

On Saturdays, the workers will be paid time-and-a-half, which means they will be paid $30 per hour (1.5 times the normal rate of $20 per hour).

So the labor cost for each worker on Saturdays will be:

$30/hour/worker × 8 hours/worker = $240/worker

For the whole crew, the labor cost for Saturdays will be:

$240/worker × 6 workers = $1,440/week

So the new total labor cost per week will be:

240 hours/week × $20/hour/worker × 6 workers + $1,440/week = $30,240/week

To calculate the revised expected duration of the project, we need to divide the total number of hours required for the project by the total number of hours worked per week, including the Saturday overtime:

2,640 hours ÷ (240 hours/week + 48 hours/week) = 9.23 weeks

So the revised expected duration of the project is approximately 9.23 weeks.

The added cost due to the acceleration is the difference between the total labor cost for the original schedule and the total labor cost for the accelerated schedule:

$30,240/week - $28,800/week = $1,440/week

Over the 9.23 weeks of the accelerated schedule, this added cost will be:

$1,440/week × 9.23 weeks = $13,315.20

So the added cost due to the acceleration is approximately $13,315.20.