A retailer is considering investing a $$50,000$ budget in one of two products. Product A has high volatility and can earn up to $50\%$ in favorable markets, but may lose up to $60\%$ in unfavorable markets. Product B has low volatility and can earn up to $30\%$ in favorable markets and may lose up to $15\%$ in unfavorable markets.

Based on this information, answer the following

a$)$ What is the decision according to the maximax criterion?

b$)$ What is the decision according to the maximin criterion?

c$)$ What is the decision according to the minimax regret criterion?

Should the retailer buy product A according to the maximum expected return criterion if they believe there is an $80\%$ chance of good markets and a $20\%$ chance of bad markets?