Drivers versus driverlessinput optimization

We are trying to stay ahead of the movement towards driverless vehicles, and I would like you to conduct some analysis around the optimal mix of drivers, versus 100% driverless autonomous vehicles. Our tech futures and heat map teams have forecasted that when autonomous vehicles are a viable option to begin to mix into our fleets our production function to cover one-hour of rides in a 30 block radius will be Q=2 D^1/2 A^1/2. Where A denotes autonomous vehicles and D denotes traditional Uber drivers. Thus, we are flexible in our proportion of traditional drivers to autonomous vehicles.

Furthermore our finance team forecasts that we will be able to negotiate autonomous vehicle rental rates between a low of $2 per hour to a high of $4.50 per hour. Currently, our traditional Uber drivers are billing out at an average of $9 per hour.

In your analysis I want you to hold the 30 block radius constant (Q=30) and analyze what our optimal cost minimizing input mixes would be under the different autonomous vehicle rental rates. Specifically, under each rental rate scenario ($2 versus $4.50) I am interested in knowing the amount of autonomous vehicles (A) and the amount of traditional drivers (D) to employ, as well as the anticipated total cost.

Think of D as capital (K) the relatively more expensive input and think of A as labor (L) the relatively cheaper input...you will see that:

MPA/MPD = D/A = r/w

When r=$2, you will find that A=4.5D

When r=$4.5, you will find that A=2D