Question

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, 12% for personal loans, and 10% 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.

Fill in the blanks

(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 H + P + A s.t.          H + P + A ≥ Minimum Home Loans H + P + A ≤ Personal Loan Requirement H + P + A = Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Allocation Home $________ Personal $________ 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. %_______ (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? - Select your answer: Yes or No Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (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. $_________ How much would the annual percentage return change? If required, round your answer to two decimal places. %________

Answer 1

Solution:

Solution to determine the optimal solution: objective of a linear programming is to maximize profit where, H = Amount allocated to home loans Pu Amount allocated to personal loans A- Amount allocared to automobile loons a) Max Pro Fit = 0.07H +0.12p +0.1A ... 0 Such that H+P+A= 1,000,000 Amount of New funds 0.6H-0.4P-0.4A7,0 Minimum Home loans P-O.GALO Personal loan Requirement b) Allocation mode to each type of loans: Loan Tupe Allocation Home $400000 Personal $2250000 Automobile $375000 Max profit -0.07H +0.120+ 0.1A = 0.070400 000)+0.12 (227000)+ 0.10(3 75000) - 92500 Total annual retuun = $92500 ? In percentage 9.210% 79,25% c) The role of Home loans is incrased to 9% The objective coefficient range for H will be "No Lower limit to 0.101" since 9% or 10.09) is within the longe Hence the soluton obtained in part b) will not change. -NO al) Tolal amount of new fund available is increased by 410,000. The dual value for constraint 1 is 0.089. The right hand sicke tonge for constraint 1 iso to NO lepper Limit: 0.089(10,000) = $890 es for this second constain will change -0.614 -0.39p - 0:34 A >,0 New op Himat Solution is H - $390,000 P = $228,750 A: $ 381,200 max propit = 0.071 +0.12P+ 0.1A - 0.07( 390,000) +0.126228750) +0.1(38120) = $9%845 92876 Total Annual veturn - $92875 In percentage 9.2875% N 9,28%

Solution to determine the optimal solution: objective of a linear programming is to maximize profit where, H = Amount allocated to home loans Pu Amount allocated to personal loans A- Amount allocared to automobile loons a) Max Pro Fit = 0.07H +0.12p +0.1A ... 0 Such that H+P+A= 1,000,000 Amount of New funds 0.6H-0.4P-0.4A7,0 Minimum Home loans P-O.GALO Personal loan Requirement b) Allocation mode to each type of loans: Loan Tupe Allocation Home $400000 Personal $2250000 Automobile $375000 Max profit -0.07H +0.120+ 0.1A = 0.070400 000)+0.12 (227000)+ 0.10(3 75000) - 92500 Total annual retuun = $92500 ? In percentage 9.210% 79,25% c) The role of Home loans is incrased to 9% The objective coefficient range for H will be "No Lower limit to 0.101" since 9% or 10.09) is within the longe Hence the soluton obtained in part b) will not change. -NO al) Tolal amount of new fund available is increased by 410,000. The dual value for constraint 1 is 0.089. The right hand sicke tonge for constraint 1 iso to NO lepper Limit: 0.089(10,000) = $890 es for this second constain will change -0.614 -0.39p - 0:34 A >,0 New op Himat Solution is H - $390,000 P = $228,750 A: $ 381,200 max propit = 0.071 +0.12P+ 0.1A - 0.07( 390,000) +0.126228750) +0.1(38120) = $9%845 92876 Total Annual veturn - $92875 In percentage 9.2875% N 9,28%