1. (18 points) A rm must choose total employee hours 6 and robot hours k knowing that the hourly wage is $20, hourly robot rental rate is $10, and total quantity pro~ duced will be q = f (k, If). The robot must at all times be supervised by the employee. Each unit of output can be sold at a price 35p, which the firm takes as given. a) (2 points) Formally write the rm's prot maximisation problem. b) (2 points) How would you conrm this problem has a maximum? c) (4 points) How would you find optimal employee and robot hours? (Someone should be able to do so by following your answer exactly.) The optimum is the critical point (k*, 3*, y*), where y" > 0. For the rest of the problem, assume the firm is at the optimum and justify your answers. d) (2 points) How do employee hours compare to robot hours? e) (4 points) By about how much do maximised prots change in the following scenarios, all else equal? 0 The firm can leave the robot unattended for one hour. 0 The robot rental rate increases to $11 / hour. f) (4 points) Compute the derivative that describes how optimal employee hours 13* move with the hourly wage rate. A 1-- n