Adirondack Savings Bank $($ASB$)$ has $$1$ million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are $6\%$ for home loans, $12\%$ for personal loans, and $7\%$ for automobile loans. The bank$$s planning committee has decided that at least $40\%$ of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed $60\%$ of the amount allocated to automobile loans.