Two capacities, one answer
Weight the package mix and you get two averages rather than one. The technician hours per vehicle come out at 2.36 on the mix in the form; the bay hours come out at 2.69, because every package holds its bay for a while with nobody working on it. Three technicians over an eight hour day allow 10.2 vehicles. Three bays over the same day allow 8.9. The shop does 8.9, and the technicians run at 88 percent of what they could do, which is an eighth of a paid day with nowhere to put a car.
That is the entire model, and it is worth doing before adding staff. On these numbers a fourth technician changes the daily throughput by exactly nothing, because the bays were the problem the whole time. A fourth bay adds 1.25 vehicles a day without hiring anybody, and one of each adds 2.97.
The gap is made of waiting
Bay hours exceed labour hours by 0.33 of an hour per vehicle here — 14 percent more bay time than hands-on time. That gap is dwell, cure and the car nobody has collected yet, and it is invisible on a timesheet because nobody is clocked on it. It is also not evenly spread: the express wash contributes six minutes of it, the correction and coating package contributes an hour.
Which means the mix moves the constraint. A shop that takes on more coating work is adding bay hours faster than it is adding labour hours, and will hit the bay wall well before it hits the staffing one. The usual symptom is a shop that feels busy and looks half empty, with finished cars parked in the working space.
Ten percent of the cars, a third of the labour
The correction package is a tenth of the vehicles through the door and 38 percent of the technician hours. The express wash is 55 percent of the vehicles and 17 percent of the hours. That ratio is worth checking against what the shop feels like, because scheduling attention tends to follow vehicle count and cost follows hours, and those two rankings are almost reversed here.
What the number is not
It is a ceiling, not a forecast. It assumes work arrives evenly through the day, that a technician can always move to whatever is ready next, that a finished car leaves its bay immediately and that nothing is waiting on a part, a customer or the weather. Every one of those fails regularly, and each failure costs capacity that this arithmetic hands you for free.
The honest way to use it is as a comparison rather than a prediction. Run it at today's mix, then at the mix you are trying to sell, and look at which constraint moves. That comparison survives all the assumptions above, because they are wrong in the same direction both times.
Questions people ask
How many cars a day can a three bay detail shop do?
On the mix in the form, 8.9 — and the limit is the bays rather than the three technicians, who could have handled 10.2. Change the mix towards longer packages and the bay figure falls faster than the labour figure does. The answer depends far more on what you are selling than on how many bays are in the building.
Why are bay hours higher than labour hours?
Because a vehicle occupies its bay while it dwells, cures or waits to be collected, and nobody is working on it during any of that. Here the gap is 0.33 of an hour per vehicle, 14 percent more bay time than hands-on time, and it is concentrated in the long packages: six minutes on an express wash against a full hour on a correction and coating.
Should I hire another technician or build another bay?
The page answers it by recomputing both. On these figures one more technician changes the daily throughput by nothing at all, because the bays were binding first, while one more bay adds 1.25 a day. Swap the mix towards short jobs and that inverts. It is worth rerunning whenever the package mix shifts.
Which package uses the most of my shop?
Not the one that comes through most often. The correction and coating package is 10 percent of the vehicles and 38 percent of the technician hours; the express wash is 55 percent of the vehicles and 17 percent of the hours. Vehicle count and hours rank the packages in almost opposite orders, which is worth knowing before deciding what to promote.
Is this what my shop will actually do?
No. It is a steady-state ceiling that assumes work arrives evenly, technicians can always move to the next ready job, finished cars leave their bays immediately and nothing waits on a part or a customer. All four fail in real shops. Use it to compare two mixes or two shop layouts rather than to fill a schedule, because the assumptions are wrong in the same direction in both runs.