A factory is suspected of hiring illegal immigrants as workers. The authority is deciding whether to conduct an inspection. If the factory has illegal workers and in inspection takes place, the workers will be discovered. The cost of an inspection to the government is 100. The benefit from the inspection is 500 if illegal workers are found, but 0 if none are found. The payoff to the authority from conducting an inspection is the benefit minus the cost, while the payoff from not inspecting is 0. For the factory, the payoff from having illegal workers and not getting caught is 200, from not using illegal workers is 0, and from using illegal workers and getting caught is -300. A factory must decide whether or not to use illegal workers, and the government must decide whether or not to conduct an inspection. a)Derive the best-response functions of the factory and the government and find all Nash equilibria. b)Plot the best-response functions and show all Nash equilibria on the graph.