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You are managing a design project. The initial estimate of work hours required was 3,860. You have 4 engineers assigned to the project full time (8 hours per day, 5 days per week) and one engineer assigned to the project half-time (4 hours per day, 5 days per week). Each engineer's work is charged to the project at $30 per hour.

At the end of 13 weeks, 65% of the design work has been completed at a cost of $62,000.

What would the duration (in weeks) of the project be based on the original estimate of work hours?

Answer :

Final answer:

The duration of the project based on the original estimate of work hours would be approximately 21.44 weeks.

Explanation:

To calculate the duration of the project based on the original estimate of work hours, we can use the formula:

Duration = (Total estimated work hours / Work completed per week) * (100 / Completion percentage)

Given:

  • Total estimated work hours: 3,860
  • Number of engineers working full time: 4
  • Number of hours worked by each full-time engineer per week: 8 hours/day * 5 days/week = 40 hours/week
  • Number of engineers working half-time: 1
  • Number of hours worked by the half-time engineer per week: 4 hours/day * 5 days/week = 20 hours/week
  • Cost per hour for each engineer: $30
  • Completion percentage: 65%

First, let's calculate the total work completed per week:

Total work completed per week = (Number of full-time engineers * Hours worked by each full-time engineer per week) + (Number of half-time engineers * Hours worked by the half-time engineer per week)

Total work completed per week = (4 * 40) + (1 * 20) = 160 + 20 = 180 hours

Now, let's calculate the duration of the project:

Duration = (Total estimated work hours / Total work completed per week) * (100 / Completion percentage)

Duration = (3,860 / 180) * (100 / 65)

Duration = 21.44 weeks (rounded to two decimal places)

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