$(11$ marks in total$)$ MyBusinessCom is inquiring whether to extend an $$80,000$ credit

to a potential new customer. Very often, the following categories are used for the credit$-$

worthiness of a credit seeker: poor risk, average risk, and good risk. Based on historical data, $25$

percent of credit seekers similar to the new potential customer are poor risks, $50$ percent are

average risks, and the remaining are good risks. If credit is granted, the expected profit for poor

risks is $-$$$10,000,$ for average risks $$15,000,$ and good risks $$25,000.$ The company may consult a

credit$-$rating organization for a fee of $$7,000$ per case evaluated.

$2$

$($a$)(4$ marks$)$ Develop a decision analysis formulation of this problem by identifying the

decision alternatives, the states of nature, and the pay$-$off table when the credit$-$rating

organization is not used.

$($b$)(5$ marks$)$ Find the EVPI.

$($c$)(2$ marks$)$ Does your answer in $($b$)$ indicate that consideration should be given to using

the credit$-$rating organization? Justify