Adirondack Savings Bank $($ASB$)$ has $$7$ 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 $7\%$ for home loans, $12\%$ for personal loans, and $9\%$ 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.

a$)$Suppose the total amount of new funds available is increased by $$50,000.$ What effect would this have on the total annual return? Explain. $($Round your answer to the nearest dollar.$)$

Increasing the amount of new funds available by $$50,000$ will increase the total annual return $($in dollars$)$ by $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)$ Assume that ASB has the original $$7$ million in new funds available and that the planning committee has agreed to relax the requirement that at least $40\%$ of the new funds must be allocated to home loans by $1\%.$ How much would the annual return change $($in dollars$)?\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

How much would the annual percentage return change? $($Round your answer to two decimal places.$)\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\%$