Re: Some math...
I'm not sure about your math, but 5520 x 0.5 hours per day = 2760 hours saved. 2760 hours per day divided by 345 would mean that these "extra" officers were working 8 hours/day, which is about spot on.
NZ$304m productivity savings over 10 years = 304m / 10 / 345 = average cost of employing an officer NZ$88k, which sounds about right (they don't get paid that, but it includes taxes, pensions and the cost of space at police stations).
NZ$159 includes hardware, software and support. Replacing all of the devices every year would only cost about NZ$80m, so you could afford to employ roughly 80 support staff/programmers per year inside of that budget.