Credit Union Fund Allocation. The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk$-$free securities to stabilize income. The various revenue$-$producing investments together with annual rates of return are as follows. LO $2$

Type of Loan$/$Investment

Annual Rate of Return $(\%)$

Automobile loans

$8$

Furniture loans

$10$

Other secured loans

$11$

Signature loans

$12$

Risk$-$free securities

$9$

The credit union will have $$2$ million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:

Risk$-$free securities may not exceed $30\%$ of the total funds available for investment.

Signature loans may not exceed $10\%$ of the funds invested in all loans $($automobile$,$ furniture, other secured, and signature loans$).$

Furniture loans plus other secured loans may not exceed automobile loans.

Other secured loans plus signature loans may not exceed the funds invested in risk$-$free securities$.$

How should the $$2$ million be allocated to each of the loan$/$investment alternatives to maximize total annual return?

What is the projected total annual return?