Suppose that the federal government wants to temporarily offer tax cuts and fee reductions to licensed producers $($LPs$)$ of cannabis on a case$-$by$-$case basis. The government wants to greatly lower taxes for struggling LPs but merely reduce some fees for financially stable LPs$.$ It estimates that $70\%$ of the LPs are struggling and $30\%$ are financially stable. However, it cannot easily tell which LPs are in each category without auditing their financial records.$$Each LP knows whether it is stable or struggling. Given this knowledge, the LP will request either lower taxes or reduced fees.$$After receiving the LP$$s request, the federal government must decide whether to grant the request or audit the LP$.$ If the LP merely requests a fee reduction, the government will always grant the request. If the LP requests a tax cut, the government can choose to either grant the request or to audit the LP$.$ Auditing a company that is truly struggling is a waste of resources; but if the audit finds the LP is truly stable, the government can safely refuse its request.$$The payoffs will be as follows.$$a$.$ If the LP is struggling, and it requests reduced fees, then the LP payoff will be $128$ and the government payoff will be $72.$b$.$ If the LP is struggling, and it requests lower taxes, and the government grants the request, then the LP payoff will be $168$ and the government payoff will be $52.$c$.$ If the LP is struggling, and it requests lower taxes, and the government conducts an audit, then the LP payoff will be $148$ and the government payoff will be $32.$d$.$ If the LP is stable, and it requests reduced fees, then the LP payoff will be $108$ and the government payoff will be $60.$e$.$ If the LP is stable, and it requests lower taxes, and the government grants the request, then the LP payoff will be $188$ and the government payoff will be $40.$f$.$ If the LP is stable, and it requests lower taxes, and the government conducts an audit, then the LP payoff will be $88$ and the government payoff will be $96.$

What should struggling LPs request, and what will be their expected payoffs?$$ii$.$ What should stable LPs request, and what will be their expected payoffs?$$iii$.$ How should the government respond to requests, and what will be its expected payoff?$$iv$.$ What percentage of all requests will involve a stable LP getting audited by the government?