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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?

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

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