Problem 9-07 (Algorithmic) As part of the settlement for a classaction lawsuit, Hoxworth Corporation must provide sufficient cashto make the following annual payments (in thousands of dollars):Year 1 2 3 4 5 6 Payment 195 220 270 320 350 470 The annualpayments must be made at the beginning of each year. The judge willapprove an amount that, along with earnings on its investment, willcover the annual payments. Investment of the funds will be limitedto savings (at 3.5% annually) and government securities, at pricesand rates currently quoted in The Wall Street Journal. Hoxworthwants to develop a plan for making the annual payments by investingin the following securities (par value = $1000). Funds not investedin these securities will be placed in savings. Security CurrentPrice Rate (%) Years to Maturity 1 $1045 6.85 3 2 $1000 5.525 4Assume that interest is paid annually. The plan will be submittedto the judge and, if approved, Hoxworth will be required to pay atrustee the amount that will be required to fund the plan. Uselinear programming to find the minimum cash settlement necessary tofund the annual payments. Let F = total funds required to meet thesix years of payments G1 = units of government security 1 G2 =units of government security 2 Si = investment in savings at thebeginning of year i Note: All decision variables are expressed inthousands of dollars. If required, round your answers to fivedecimal places. For subtractive or negative numbers use a minussign even if there is a + sign before the blank. (Example: -300)Min F s.t. F + G1 + G2 + S1 = G1 + G2 + S1 + S2 = G1 + G2 + S2 + S3= G1 + G2 + S3 + S4 = G2 + S4 + S5 = S5 + S6 = Round your answer tothe nearest dollar. If an amount is zero, enter "0". Currentinvestment required $ Investment in government security 1 $Investment in government security 2 $ Investment in savings foryear 1 $ Investment in savings for year 2 $ Investment in savingsfor year 3 $ Investment in savings for year 4 $ Investment insavings for year 5 $ Investment in savings for year 6 $ Use thedual value to determine how much more Hoxworth should be willing topay now to reduce the payment at the beginning of year 6 to$400,000. Round your answer to the nearest dollar. $ Use the dualvalue to determine how much more Hoxworth should be willing to payto reduce the year 1 payment to $150,000. Round your answer to thenearest dollar. Hoxworth should be willing to pay anything lessthan $ . Suppose that the annual payments are to be made at the endof each year. Reformulate the model to accommodate this change.Note: All decision variables are expressed in thousands of dollars.If required, round your answers to five decimal places. Forsubtractive or negative numbers use a minus sign even if there is a+ sign before the blank. (Example: -300) Min F s.t. 1) F + G1 + G2+ S1 = 2) G1 + G2 + S1 + S2 = 3) G1 + G2 + S2 + S3 = 4) G1 + G2 +S3 + S4 = 5) G2 + S4 + S5 = 6) S5 + S6 = 7) S6 + S7 = How muchwould Hoxworth save if this change could be negotiated? Round youranswer to the nearest dollar. $ PreviousNext