The credit union will have $$2,400,000$ 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 the automobile loans.

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

How should the $$2,400,000$ be allocated to each of the loan$/$investment alternatives $($in dollars$)$ to maximize total annual return?

Automobile loans $

Furniture loans $,$$

Other secured loans $

Signature loans $

Risk$-$free securities $

What is the projected total annual return $($in dollars$)?$

$ Please give numerical answers for the questions.