investments together with annual rates of return are as follows:

$\backslash$table$[[$Type of Loan$/$Investment Annual Rate of Return $(\%),],[$Automobile loans,$7],[$Furniture loans,$10],[$Other secured loans,$11],[$Signature loans,$12],[$Rlsk$-$free securities$,8]]$

The credit union will have $$2\mathrm{.}3$ million available for investment during the coming year. State laws and credit union policies impose the following restrictlons 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\mathrm{.}3$ million be allocated to each of the loan$/$investment alternatives to maximize total annual return?

$\backslash$table$[[\backslash$table$[[$Type of$],[$Loan$/$Investment$]],\backslash$table$[[$Fund$],[$Allocation$]]],[$Automobile loans,$$690,001$