Acme Incorporated has $$20$ million to invest. The company$$s CEO has three investment options: expand production; invest in stocks; or buy deposit certificates. The return from expanding production or investing in stocks depends on whether the economy continues to boom or enters a recession. The CEO estimates that there is a $30\%$ chance of a recession. She also estimates that:

$>$ expanding production will generate a positive return of $15\%$ if the economy continues to boom and a loss of $10\%$ if the economy enters recession;

$>$ investing in stocks will generate a positive return of $12\%$ if the economy continues to boom and a loss of $5\%$ if the economy enters recession; and

$>$ investing in bank deposit certificates will generate a positive return of $6\%$ independent of economic conditions.

a$.$ What decision should the CEO make if she uses the maximin strategy? Explain.

b$.$ What decision should the CEO make if she uses the maximax strategy? Explain.

c$.$ What decision should the CEO make if she wants to maximize the expected profit of the investment? Explain.