Portfolio Optimization Model

You have been hired as a financial advisor to optimize a client's investment portfolio. The

client has expressed interest in investing in the following asset classes:

Stocks $($S$)$: Expected annual return of $12\%$ and a risk score of $8.$

Bonds $($B$)$: Expected annual return of $6\%$ and a risk score of $3.$

Real Estate $($R$)$: Expected annual return of $10\%$ and a risk score of $6.$

Commodities $($C$)$: Expected annual return of $8\%$ and a risk score of $5.$

The client has specific requirements and constraints:

The total investment amount is $$1,000,000.$

No more than $50\%$ of the total investment should be allocated to stocks due to high

volatility.

The investment in bonds should be at least $20\%$ of the total investment.

The combined investment in real estate and commodities should not exceed $40\%$ of the

total investment.

The client's risk tolerance is such that the total weighted risk score $($risk score multiplied

by the percentage of investment in each asset$)$ must not exceed $5.$

Formulate a linear programming model to help the client achieve maximum expected annual

return while satisfying the above constraints. Then, use Excel Solver to determine the optimal

investment amounts for each asset class.