: A car manufacturer plans to produce four different brands of cars. Three possible economic conditions may exist in the future. The three states are Favorable, Stable, and Unfavorable. Their probabilities are respectively 0.55, 0.35, and 0.10. The payoffs are the estimated sales in million dollars (Use two decimals, do not round even if you get decimal values)

	States of nature
	Favorable	Stable	Unfavorable
Toyota	600	-200	300
Honda	300	450	250
Audi	600	600	-200
Volkswagen	-200	400	600

The manufacturer can produce only one brand, given the company's financial circumstances. Considering the current information,

a.) Recommend the manufacturer to choose the brand using the expected value approach and find the expected sales revenue

b) Recommend the manufacturer to choose the brand using the expected opportunity loss method and provide expected regret value.

c) The company can increase its sales revenue if they hire an agency (or informer or supernatural person) to give perfect information about the states. If hired, the company must pay $10m to the agency. Decide to hire or not. In both scenarios, find the new sales revenue for the company. Also, find an increase in sales revenue, if any.