National Insurance Associates carries an investment portfolio of stocks, bonds, and other investment alternatives. Currently $200,000 of funds are available and must be considered for new investment opportunities. The four stock options National is considering and the relevant financial data are as follows;

The risk measure indicates the relative uncertainty associated with the stock in terms of its realizing the projected annual return; higher values indicate greater risk. The risk measures are provided by the firms top financial advisor. Nationals top management has stipulated the following investment guidelines: The annual rate of return for the portfolio must be at least 9% and no one stock can account for more than 50% of the total dollar investment.

Provide a mathematical model.

\begin{tabular}{lcccc} & \multicolumn{4}{c}{ Stock } \\ & A & B & C & D \\ Price per share & $100 & $50 & $80 & $40 \\ Annual rate of return & 0.12 & 0.08 & 0.06 & 0.10 \\ Risk measure per dollar invested & 0.10 & 0.07 & 0.05 & 0.08 \end{tabular}