Problem $13-22($Algo$)$ Portfolio effect of a merger $[$L$013-5]$

Treynor Pie Company is a food company specializing in high$-$calorie snack foods. It is seeking to diversify its food business and lowe its risks. It is examining three companies$-$a gourmet restaurant chain, a baby food company, and a nutritional products firm. Each of these companies can be bought at the same multiple of earnings. The following represents information about all the companies.

$\backslash$table$[[$Company$,\backslash$table$[[$Correlation$],[$with Treynor$],[$Pie Company$]],\backslash$table$[[$Sales $($$$],[$millions$)]],\backslash$table$[[$Expected$],[$Earnings $($$$],[$millions$)]],\backslash$table$[[$Standard$],[$Deviation in$],[$Earnings $($ $