Q$1.$ An investor is considering allocating $$10,000$ among five investment alternatives. The five

alternatives and their respective fund categories, risk levels, and average annual returns are

shown below:

The risk level of each investment is rated on a scale of $1$ to $5,$ where $1$ is very conservative and $5$

is very risky. The investor would like to maximize the average annual return on his

investment subject to the following restrictions:

The average risk level of the entire investment should not exceed $2\mathrm{.}5.$ The average here is a

weighted average in terms of the amount of money invested in each fund.

$30\%-35\%$ of the investment should be placed in money market funds. In other words, you

should invest at least $30\%$ and at most $35\%$ of the budget into the money market funds

At most $$3,000$ should be invested in the aggressive growth fund.

Construct and solve a linear optimization model to determine the optimal allocation of the

investor's money. The decision variables, A$,$ B$,$ C$,$ D and E$,$ are defined as the amount of

money you will invest into Adams, Barney, Chilton, Dunster and Excelsior, respectively.

Please write down your mathematical model using the decision variables A$,$ B$,$ C$,$ D and E defined.