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 loan to maximize the total annual return for the new funds. (Assume / 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 0.07H + 0.12P + 0.09A S.t. Available investment funds H + P + A = 5000000 Minimum home loan amount H > 2000000 Maximum personal loan amount P - 0.6A