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 7% for home loans, 14% for personal loans, and 11% 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 50% 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. If the constant is "1" it must be entered in the box. If your answer is zero enter "O". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max 0.07 H+ 0.14 P + 0.11 A s.t. 1 H + 1 P+ 1 A > -10000 Minimum Home Loans -1 H + O P + 0 As -40000 Personal Loan Requirement OH + 1 P + -0.6 A = 0 Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Allocation Home $ 400000 Personal $ 225000 Automobile $ 375000 What is the total annual return? If required, round your answer to nearest whole dollar amount. $ 88750 What is the annual percentage return? If required, round your answer to two decimal places. 8.875 % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? Select your answer (d) Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain. If required, round your answer to nearest whole dollar amount. An increase of $10,000 to the total amount of funds available would increase the total annual return by $ (e) Assume that ASB has the original $1 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? If required, round your answer to nearest whole dollar amount. S How much would the annual percentage return change? If required, round your answer to two decimal places. % 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 7% for home loans, 14% for personal loans, and 11% 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 50% 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. If the constant is "1" it must be entered in the box. If your answer is zero enter "O". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max 0.07 H+ 0.14 P + 0.11 A s.t. 1 H + 1 P+ 1 A > -10000 Minimum Home Loans -1 H + O P + 0 As -40000 Personal Loan Requirement OH + 1 P + -0.6 A = 0 Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Allocation Home $ 400000 Personal $ 225000 Automobile $ 375000 What is the total annual return? If required, round your answer to nearest whole dollar amount. $ 88750 What is the annual percentage return? If required, round your answer to two decimal places. 8.875 % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? Select your answer (d) Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain. If required, round your answer to nearest whole dollar amount. An increase of $10,000 to the total amount of funds available would increase the total annual return by $ (e) Assume that ASB has the original $1 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? If required, round your answer to nearest whole dollar amount. S How much would the annual percentage return change? If required, round your answer to two decimal places. %
