Problem 9-07 (Algorithmic) As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): Year 1 2 3 4 5 6 Payment 170 210 250 310 340 500 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the unds will be limited to savings at 3.25% annual n me all Street and government securities, a prices and ates curren quote Journal. Hoxworth wants to develop a plan for making the annual payments by investing in the following securities (par value $1000). Funds not invested in these securities will be placed in savings. Security Current Price Rate (%)|Years to Maturity $1075 6.55 1000 5.125 2 4 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan annual payments. D a. Use linear programming to find the minimum cash settlement necessary to fund the a not round your answers. If required, only round your decision variables to a whole dollar amount. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) Let F = total funds required to meet the six years of payments G1-units of government security 1 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan a. Use linear programming to find the minimum cash settlement necessary to fund the annual payments. Do not round your answers. If required, only round your decision variables to a whole dollar amount. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Let F= total funds required to meet the six years of payments G1units of government security1 G2units of government security 2 Si investment in savings at the beginning of year i Note: All decision variables are expressed in thousands of dollars Min F 2) X S21= 3) 4) 5) 6) Current investment required Investment in government security 1 $ Investment in government security 2 Investment in savings for year 1 Investment in savings for year 2 Investment in savings for year 3 Investment in savings for year 4$ Investment in savings for year 5$ Investment in savings for year 6 $ b. Use the shadow price to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000 c.Use the shadow price to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000 Hoxworth should be willing to pay anything less than $ d. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Do not round your answers. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) Note: All decision variables are expressed in thousands of dollars. d. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Do not round your answers. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) Note: All decision variables are expressed in thousands of dollars Min G2 + 2) G2 + 3) G2 + S3+ S4 4) G2 + S51= 5) 6) S5 + 7) S6+ How much would Hoxworth save if this change could be negotiated? If required, round your answer to a whole dollar amount. Problem 9-07 (Algorithmic) As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): Year 1 2 3 4 5 6 Payment 170 210 250 310 340 500 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the unds will be limited to savings at 3.25% annual n me all Street and government securities, a prices and ates curren quote Journal. Hoxworth wants to develop a plan for making the annual payments by investing in the following securities (par value $1000). Funds not invested in these securities will be placed in savings. Security Current Price Rate (%)|Years to Maturity $1075 6.55 1000 5.125 2 4 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan annual payments. D a. Use linear programming to find the minimum cash settlement necessary to fund the a not round your answers. If required, only round your decision variables to a whole dollar amount. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) Let F = total funds required to meet the six years of payments G1-units of government security 1 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan a. Use linear programming to find the minimum cash settlement necessary to fund the annual payments. Do not round your answers. If required, only round your decision variables to a whole dollar amount. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Let F= total funds required to meet the six years of payments G1units of government security1 G2units of government security 2 Si investment in savings at the beginning of year i Note: All decision variables are expressed in thousands of dollars Min F 2) X S21= 3) 4) 5) 6) Current investment required Investment in government security 1 $ Investment in government security 2 Investment in savings for year 1 Investment in savings for year 2 Investment in savings for year 3 Investment in savings for year 4$ Investment in savings for year 5$ Investment in savings for year 6 $ b. Use the shadow price to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000 c.Use the shadow price to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000 Hoxworth should be willing to pay anything less than $ d. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Do not round your answers. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) Note: All decision variables are expressed in thousands of dollars. d. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Do not round your answers. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) Note: All decision variables are expressed in thousands of dollars Min G2 + 2) G2 + 3) G2 + S3+ S4 4) G2 + S51= 5) 6) S5 + 7) S6+ How much would Hoxworth save if this change could be negotiated? If required, round your answer to a whole dollar amount