Using Bayesian Decision Theory, solve the problem presented below. The purpose of this is to deepen your understanding of the "Value of Research" issue.

Quicken Business Software is considering introducing a new product, the mid$-$market SalesMgrPro. If the product is a big success, Quicken will make an extra $$6$ million in profit and a failure will result in a loss of $$3$ million. Not introducing this product will not change Quicken's profit from what it is today. The probability of each outcome is estimated at: big success $65\%,$ failure $35\%.$ Quicken's marketing manager is considering doing a concept test before making the decision. She knows that the test is not $100\%$ accurate, in fact she knows from previous experience that for successful products the concept test approach is $80\%$ positive and for failure products the test is $65\%$ negative. $($a$)$ If she does not do marketing research, should Quicken introduce SalesMgrPro, and why? $($b$)$ Should Quicken introduce without research, not introduce without research, or conduct the concept test? $($c$)$ What is the maximum amount the marketing manager should spend on the concept test?

$($For this question, you can draw the decision tree manually and scan it$)$