As the chief investment officer for a money management firm specializing in taxable individual investors, you are trying to establish a strategic asset allocation for two different clients.You have established that Ms$.$ A has a risk$-$tolerance factor of $8,$ while Mr$.$ B has a risk$-$tolerance factor of $27.$ The characteristics for four model portfolios follow:

a$.)$ Calculate the expected utility of each prospective portfolio for each of the two clients.

b$.)$ Which portfolio represents the optimal strategic allocation for Ms$.$ A$?$ Which portfolio is optimal for Mr$.$ B$?$Explain why there is a difference in these two outcomes.

c$.)$ For Ms$.$ A$,$ what level of risk tolerance would leave her indifferent between having Portfolio $1$ or Portfolio $2$ as her strategic allocation? Demonstrate.