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.

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$)?$