3. Nike purchases footballs in batches of 180 from its supplier. The supplier tends to have "good" batches 82% of the time where only 5% of the footballs are defective and bad batches 18% of the time where 30% of the footballs are defective. It costs Nike $80 to d with a defective football. Before the footballs ship, Nike is considering having a person inspect each football where each defective one can be replaced for free. The cost to insp each football is $8. 1. Develop a decision analysis formulation for this problem (define the states of nature, alternatives, and the payoff table. 2. What decision should be made according to the maximax decision rule? 3. What decision should be made according to the maximin decision rule? 4. What decision should be made according to the minimax regret decision rule? 5. What decision should be made according to the expected value decision rule?