We produce Lidar units that are used as an input in Uber's driverless car fleet, and we are needing to ramp up our daily production to 135. We have secured a new higher capacity production facility and relocated the necessary capital equipment, and we would like you to decide how to staff the new facility. For producing 135 Lidar units we estimate our production function to be Q = 5(S1/2)(U1/2), where U are unskilled workers that we historically pay an hourly wage of $8, and S are Specialists that we historically pay an hourly wage of $72.

I used to run these projections back when I was line manager, and I recall that our MRTS = MPU/MPS, so we get (2.5)(S1/2)(U-1/2) / (2.5)(S-1/2)(U1/2) which simplifies down to S/U. Using the MRTS = WU/WS rule we can get: S/U = 8/72= 1/9. Thus, our unskilled workers should be 9 times more than our specialists (U = 9S), but I do not remember how to extract the exact number of each labor input. So, I am counting on you to let me know how many unskilled workers (U) and how many Specialists (S) to employ in order to minimize costs of producing 135 Lidar units. Please make sure to report what the anticipated total daily cost of labor will be. I am assuming that our labor continues to work hard for us and exert max effort in the new facility. However, its generally a longer commute to the new facility for most of our potential workers and I fear we risk a loss in employee morale. Two risk mitigation strategies are to (i) hire more workers than what you have recommended, or (ii) invest in incentive mechanisms to ensure max labor effort. How would you evaluate those two options?