Managerial Economics 6th Edition

8. The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and labor input is:

Q = -0.8 + 4.5L - 0.3L²

where Q is the number of cars washed per hour and L is the number of people employed per hour. The firm receives $5 for each car washed, and the hourly wage rate for each person employed is $4.50. The cost of other inputs like water is trivial; hence, they are ignored.

a. How many people should be employed to maximize profit?

b. What will be the firm's hourly profit?

c. Is this relationship between output and labor input valid for all values of L? Why or why not?