2) Financial Planning Problem: Annual Payments: Year 1 Payment ($k) 1 190 2 215 3 240 4 285 5 315 6 460 Annual payments must be made at the beginning of each year. Investments in the funds with be limited to savings (at 4% annual return) and bonds, at the following prices Bond Years to Maturity Market Price $1055 $1000 Rate(%) 6.750 5.125 Assume interest is paid annually and that the par value of the bonds is $1000. a) Use Linear Programming to find the minimum cash required to meet the annual payment requirements. b) Use the shadow price to determine how much the payee should be willing to pay now in order to reduce the payment at year 6 to $400,000. Hint: Use constraint 6. Use the shadow price to determine how much more the payee should be willing to pay now to reduce the year 1 payment to $150,000. Hint: Use constraint 1. 2) Financial Planning Problem: Annual Payments: Year 1 Payment ($k) 1 190 2 215 3 240 4 285 5 315 6 460 Annual payments must be made at the beginning of each year. Investments in the funds with be limited to savings (at 4% annual return) and bonds, at the following prices Bond Years to Maturity Market Price $1055 $1000 Rate(%) 6.750 5.125 Assume interest is paid annually and that the par value of the bonds is $1000. a) Use Linear Programming to find the minimum cash required to meet the annual payment requirements. b) Use the shadow price to determine how much the payee should be willing to pay now in order to reduce the payment at year 6 to $400,000. Hint: Use constraint 6. Use the shadow price to determine how much more the payee should be willing to pay now to reduce the year 1 payment to $150,000. Hint: Use constraint 1