1. (18 points) A firm must choose total employee hours and factory hours k knowing that the hourly wage is $10, hourly factory rental rate is $20, and total quantity produced will be q=f(k,). The employee must be present for all hours the factory is rented. Each unit of output can be sold at a price $p, which the firm takes as given. a) (2 points) Formally write the firm's profit maximisation problem. b) (2 points) How would you confirm this problem has a maximum? c) (4 points) How would you find optimal employee and factory hours? (Someone should be able to do so by following your answer exactly.) The optimum is the critical point (k,,), where >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 factory hours? e) (4 points) By about how much do maximised profits change in the following scenarios, all else equal? - The firm can leave the factory unattended for one hour. - The wage increases to $11 /hour. f) (4 points) Compute the derivative that describes how optimal factory hours k * move with the factory rental rate