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Productivity

I need the formula for the following: I have 39 technicians working 8 hours a day. The technicians should be loaded with 4.5 jobs per day, but are currently loaded with 2.4 jobs per day. What is the formula to find available hours?

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You need to specify if the 4.5 jobs/day are done by one technician or by all 39 technicians.
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2 Answers

I'm assuming the 4.5 and 2.4 jobs/day refers to all 39 technicians.
Total work hours: 39*8=312 hours/day
Should be doing 4.5 jobs/day, so they need 312/4.5 = 69.3 hours/job
They are doing 2.4 jobs/day, so they work 69.3*2.4 = 166 hours/day
Available hours: 312-166=146 hours (3.7 hours per technician)
Case 1: 39 technicians, 8 hours per day, 4.5 jobs per day.
 
Total hours = (39)*(8) = 312 man hours
Total jobs = (39)*(4.5) = 175.5 jobs per day
 
Therefore, each job takes 0.5625 hours. [i.e., 0.5625 hours per job)
 
Case 2: 39 technicians, X hours per day, 2.4 jobs per day.
 
We may safely assume that the number of hours to complete one job will remain constant in both cases, so that
 
[(39)*(2.4)]/[(39)*X] = 0.5625
 
[(2.4)/(X)] = 0.5625
 
(0.5625)X = 2.4
 
X = (2.4)/(0.5625) = 4.266 hours per day