The University's Employee Credit Union Has $8 Million Available for Loans

Short Answer

The University's employee credit union has $8 million available for loans in the coming year. As VP in charge of finances, you must decide how much capital to allocate to each of four different kinds of loans, as shown in the table.
$$\begin{array} { | c | c | } \hline \text { Type of Loan } & \begin{array} { c } \text { Annual Rate of } \\\text { Return }\end{array} \\\hline \text { Automobile } & 8 \% \\\hline \text { Furniture } & 10 \% \\\hline \text { Signature } & 12 \% \\\hline \text { Other secured } & 10 \% \\\hline\end{array}$$
State laws and credit union policies impose the following restrictions:
Signature loans may not exceed 10 percent of the total investment of funds.
Furniture loans plus other secured loans may not exceed automobile loans.
Other secured loans may not exceed 200 percent of automobile loans.
How much should you allocate to each type of loan to maximize the annual return
Allocate $__________ to automobile loans, $__________ to signature loans, and $__________ to any combination of furniture loans and other secured loans.