A trust officer for a major banking institution is planning

the investment of a $$1$ million family trust fund for the

coming year. The trust officer has identified a portfolio of

stocks and another group of bonds that might be selected

for investment. The family trust can be invested in stocks

or bonds exclusively, or a mix of the two. This trust officer

prefers to divide the funds in increments of $10\%$; that is$,$ the

family trust is split into the following alternatives:

$($a$)100\%$ stocks and $0\%$ bonds

$($d$)70\%$ stocks

and $30\%$ bonds

$($b$)90\%$ stocks and $10\%$ bonds

$($e$)0\%$ stocks and

$100\%$ bonds

$($c$)80\%$ stocks and $20\%$ bonds

The trust officer has evaluated the relationship between the

yields on the different investments and the general

economic conditions. Her judgment is as follows:

$(1)$ If the next year is characterized by solid growth in the

economy, bonds will yield $12\%$ and stocks $20\%$;

$(2)$ If the next year is characterized by inflation, bonds will

yield $18\%$ and stocks $10\%$

$(3)$ If the next year is characterized by stagnation, bonds

will yield $12\%$ and stocks $8\%.$

$($A$)$ Constructs the payoff and the opportunity loss table.

$($B$)$ Determine the best decision using the maximax,

maximin, Laplace, Hurwicz $(=0\mathrm{.}40)$ and minimax

regret criteria.

$($C$)$ Suppose that a leading economic forecasting firm

projects solid growth