A Credit Union Wants to Make Investments in the Following

Essay

A credit union wants to make investments in the following:
$$\begin{array} { l c } \text { Type of Investment } & \begin{array} { c } \text { Annual Rate } \\\text { of Return (\%) }\end{array} \\\hline \text { Vehicle loans } & 7 \\\text { Consumer loans } & 9 \\\text { Other secured loans } & 10 \\\text { Signature loans } & 11 \\\text { Risk-free securities } & 8 \\\hline\end{array}$$
The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply:
∙ Risk-free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total.
∙ Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans)
∙ Consumer loans plus other secured loans may not exceed the vehicle loans
∙ Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return?