Consider a pair of standard, 20° pressure angle steel gears with a .75 inch face width. The pitch diameter of the pinion is 2.00 inches. The pitch diameter of the mating gear is 6.00 inches. The gears are made from a grade of steel which exhibits an ultimate tensile strength of 120,000 psi. and which has been case hardened such that the ultimate tensile strength of the tooth surfaces is 180,000 psi. What range of values of gear pitch will result in the maximum capacity (i. e. torque or power at a specified speed) of the gear pair? You may assume values for unknown parameters which you believe are typical of industrial machinery but do not make unnecessary assumptions. Please be explicit about all assumptions and justify as appropriate.