Adirondack Savings Bank $($ASB$)$ has $$5$ million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are $7\%$ for home loans, $12\%$ for personal loans, and $9\%$ for automobile loans. The bank's planning committee has decided that at least $40\%$ of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed $60\%$ of the amount allocated to automobile loans.$($a$)$Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. $($Assume H is the amount allocated on home loans, A is the amount allocated on Auto loans, and P is the amount allocated on personal loans. Write your answers expressing the amount allocated in dollars.$)$Max Incorrect: Your answer is incorrect.s$.$t$.$Available investment funds Incorrect: Your answer is incorrect.Minimum home loan amount Incorrect: Your answer is incorrect.Maximum personal loan amount Incorrect: Your answer is incorrect.H$,$ P$,$ A $0($b$)$How much $($in dollars$)$ should be allocated to each type of loan?home loans$ Correct: Your answer is correct.personal loans$ Correct: Your answer is correct.auto loans$ Correct: Your answer is correct.What is the total annual return $($in dollars$)?$$ Correct: Your answer is correct.What is the annual percentage return? $($Round your answer to two decimal places.$)$ Correct: Your answer is correct. $\%($c$)$If the interest rate on home loans increases to $9\%,$ would the amount allocated to each type of loan change? Explain.Since $0\mathrm{.}09$ Correct: Your answer is correct. within the allowable range, the amount allocated to each type of loan obtained in part $($b$)$ Correct: Your answer is correct. change.$($d$)$Suppose the total amount of new funds available is increased by $$70,000.$ What effect would this have on the total annual return? Explain. $($Round your answer to the nearest dollar.$)$Increasing the amount of new funds available by $$70,000$ will increase the total annual return $($in dollars$)$ by $ $.($e$)$Assume that ASB has the original $$5$ million in new funds available and that the planning committee has agreed to relax the requirement that at least $40\%$ of the new funds must be allocated to home loans by $1\%.$ How much would the annual return change $($in dollars$)?$$ How much would the annual percentage return change? $($Round your answer to two decimal places.$)\%$