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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, 10% 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 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. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max s.t. H + Personal H+ H + H + P + $ P + P + A = (b) How much should be allocated to each type of loan? Loan type Home $ Allocation P+ A ΑΣ AS Automobile What is the total annual return? If required, round your answer to nearest whole dollar amount. $ What is the annual percentage return? If required, round your answer to two decimal places. Minimum Home Loans Personal Loan Requirement Amount of New Funds % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change?

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, 10% 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 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. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max s.t. H + Personal H+ H + H + P + $ P + P + A = (b) How much should be allocated to each type of loan? Loan type Home $ Allocation P+ A ΑΣ AS Automobile What is the total annual return? If required, round your answer to nearest whole dollar amount. $ What is the annual percentage return? If required, round your answer to two decimal places. Minimum Home Loans Personal Loan Requirement Amount of New Funds % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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, 10% 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 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. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max s.t. Home Personal Automobile H + H + H + % H + P + P + P + P + (b) How much should be allocated to each type of loan? Loan type Allocation 100 ▲ A A Z AS A = What is the total annual return? If required, round your answer to nearest whole dollar amount. $ What is the annual percentage return? If required, round your answer to two decimal places. Minimum Home Loans Personal Loan Requirement Amount of New Funds (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? - Select your answer
Transcribed Image Text: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, 10% 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 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. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max s.t. Home Personal Automobile H + H + H + % H + P + P + P + P + (b) How much should be allocated to each type of loan? Loan type Allocation 100 ▲ A A Z AS A = What is the total annual return? If required, round your answer to nearest whole dollar amount. $ What is the annual percentage return? If required, round your answer to two decimal places. Minimum Home Loans Personal Loan Requirement Amount of New Funds (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? - Select your answer
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