Chapter 2.5, Problem 58E

401(k) RETIREMENT PLANS Three network consultants Alan, Maria and Steven, each received a year-end bonus of $\$10,000$, which they decided to invest in a 401(k) retirement plan sponsored by their employer. Under this plan employees are allowed to place their investments in three funds, an equity index fund $\left(\text{I}\right)$, a growth fund $\left(\text{II}\right)$, and a global equity fund $\left(\text{III}\right)$. The allocations of the investments (in dollars) of the three employees at the beginning of the year are summarized in the matrix.

$\begin{array}{l}\text{Fund}\\ \text{I}\text{II}\text{III}\\ A=\begin{array}{c}\text{Alan}\\ \text{Maria}\\ \text{Steven}\end{array}\left[\begin{array}{ccc}4000& 3000& 3000\\ 2000& 5000& 3000\\ 2000& 3000& 5000\end{array}\right]\end{array}$

The returns of the three funds after one year are given in the matrix.

$B=\begin{array}{c}\text{Fund}\text{I}\\ \text{Fund}\text{II}\\ \text{Fund}\text{III}\end{array}\left[\begin{array}{c}0.18\\ 0.24\\ 0.12\end{array}\right]$

Which employee realized the best return on his or her investments for the year in question? The Worst return?