$18\mathrm{.}18$ A corporation is considering a new production process that, if efficient, will save the corporation $$350000$ a year for the next $5$ years. If it is not efficient, the amount of lost sales plus the expense of converting to the new process and then reconverting to the old will come to $$925000.$ Determine the recommended decision under the a priori criterion if the company feels that the new process has an $80$ percent chance of being efficient.

$18\mathrm{.}19$ Determine the recommended decision under the a priori criterion for the process of Problem $18\mathrm{.}16$ if$,$ in the past, the farmer has lost much of his harvest to frost one out of every $7$ years.

$18\mathrm{.}20$ Assume that prior to making a decision, the manufacturer described in Problem $18\mathrm{.}17$ pays $$1000$ for a credit rating report on the retailer. The report rates the retailer as a poor risk, but the manufacturer knows that the rating procedure is not totally reliable. The credit bureau concedes that it will rate an average risk as a poor risk $30$ percent of the time, and it will rate a good risk as a poor risk $5$ percent of the time. It will rate a poor risk correctly $90$ percent of the time. Based on these data, determine the recommended decision for the manufacturer under the a posteriori criterion.

$18\mathrm{.}21$ The corporation of Problem $18\mathrm{.}18$ has a third option available to it; namely, to integrate one stand$-$alone phase of the new process into its current process and test its efficiency before deciding whether to convert. The cost of testing the stand$-$alone phase is $$125000,$ of which $$75000$ is recoverable if the new process is adopted. If the stand$-$alone phase is not efficient, then an additional $$25000$ in sales is lost during the test.

If the entire new process is efficient, then the stand$-$alone phase should operate efficiently with probability $0\mathrm{.}99.$ If the entire new process is not efficient, the stand$-$alone phase could still operate efficiently, and the company estimates this would happen with probability $0\mathrm{.}6.$ Construct a decision tree for the entire decision process and determine the recommended actions.

Please do $18\mathrm{.}21$ depending on $18\mathrm{.}18$