1. The owner of Sudsy Car Wash believes that the relationship between the number of cars washed and the number of workers employed each hour is Q=-0.5+10.6L-1, where is the number of cars washed per hour and I is the number of workers employed, which is the only input. The company charges $20 for each car washed, which is the going competitive rate in town, and the wage rate per hour is $12. A. How many people should Sudsy employ to maximize profits? B. What will be the firm's hourly profit? 2. Your firm hires an outside consultant who advises the firm to increase employment of its production workers by 10 percent. A year later, a follow-up study is conducted that reveals the average productivity of production workers fell 5 percent after the hiring. Top management is using this study as clear evidence to lay off the additional workers. Does the study provide clear evidence that the increased employment was counter to the firm's profit-maximizing objective? A few sentences and a graph will suffice as an answer. 3. A manufacturer of automobiles plans on using 20,000 widgets in the assembly process over the next year. The firm buys widgets from a supplier who charges $50 for each lot of widgets delivered. Assume that the firm uses widgets at a constant rate throughout the year. If the cost of carrying inventories of widgets is 8 cents per unit, than what size lots of widgets should the firm order from its supplier? What is the optimal level of inventory?