Invana, an individual investor, has $$325,000$ to invest right before retiring. She is considering the following four investment options. The investment options, along with their anticipated rate of return, are identified in the table below:

Each investment alternative has a perceived risk to Invana, so she aims to diversify her portfolio while maximizing the expected return on her investment. She has identified the following guidelines to manage risk in her portfolio:

$1.$ No more than $20\%$ of the total investment should be in municipal bonds.

$2.$ The amount invested in the Local Bank CD should not exceed the amount invested in the other three alternatives.

$3.$ At least $30\%$ of the investment should be on U$.$S$.$ Treasury Bills and the Local Bank CD$.$

$4.$ To be safe, more should be invested in the Local Bank CD and the U$.$S$.$ Treasury Bills than in municipal bonds and the growth stock fund by a ratio of at least $1\mathrm{.}2$ to $1.$

a$.$ Generate a mathematical LP model to address the portfolio selection problem.

i$.$ What is the overall expected rate of return for the recommended portfolio?