A machine produces either \(2 \%, 10 \%\), or \(25 \%\) defectives. It costs \(\$ 600\) to check the machine each morning to guarantee that it will produce \(2 \%\) defectives for that day. If the machine is not checked, the extra cost created by a batch containing \(10 \%\) defectives is \(\$ 500\) and with a batch containing \(25 \%\) defectives is \(\$ 3,000\). The probability that the machine will be in a state producing a percentage of defectives of \(2 \%, 10 \%\), or \(25 \%\) is \(0.7,0.2\), and 0.1 , respectively. What should the manager decide if her objective is to minimize the expected costs?

What is the expected value of perfect information concerning the true state of nature \((2 \%, 10 \%\), or \(25 \%)\) ?