A single stage spur gear reducer is to be specified for a large industrial ventilating fan. The motor delivers 7.5 hp at a speed of 1760 rpm. The fan speed is to be about 500 rpm (± 3%). A family of economical (machined with shaping cutters) gears are available in standard pitches of 100, 80, 64, 48, 32, 24, 20, 16, 12, 10, 8, or 6 teeth per inch diameter. The bulk UTS of the manufactured steel gears is 130,000 psi and the surface hardness of the teeth is 340 BHN. Select and specify a pinion and mating gear that conform to standard limits on face width. Explicate all engineering assumptions that you make. Also be explicit as to how your final selection was made from among all of those which satisfy the design requirements.