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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# 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**

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