[SOLVED] 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):

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 funds will be limited to savings (at 3.25% annually) and government securities, at prices and rates currently quoted in The Wall Street 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
1 $1075 6.55 3
2 $1000 5.125 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.
Use linear programming to find the minimum cash settlement necessary to fund the annual payments.
Let
F = total funds required to meet the six years of payments
G1 = units of government security 1
G2 = units of government security 2
Si = investment in savings at the beginning of year i
Note: All decision variables are expressed in thousands of dollars.
If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Min F
s.t.
fill in the blank 1
F + fill in the blank 2
G1 + fill in the blank 3
G2 + fill in the blank 4
S1 = fill in the blank 5
fill in the blank 6
G1 + fill in the blank 7
G2 + fill in the blank 8
S1 + fill in the blank 9
S2 = fill in the blank 10
fill in the blank 11
G1 + fill in the blank 12
G2 + fill in the blank 13
S2 + fill in the blank 14
S3 = fill in the blank 15
fill in the blank 16
G1 + fill in the blank 17
G2 + fill in the blank 18
S3 + fill in the blank 19
S4 = fill in the blank 20
fill in the blank 21
G2 + fill in the blank 22
S4 + fill in the blank 23
S5 = fill in the blank 24
fill in the blank 25
S5 + fill in the blank 26
S6 = fill in the blank 27
Round your answer to the nearest dollar. If an amount is zero, enter “0”.
Current investment required $ fill in the blank 28
Investment in government security 1 $ fill in the blank 29
Investment in government security 2 $ fill in the blank 30
Investment in savings for year 1 $ fill in the blank 31
Investment in savings for year 2 $ fill in the blank 32
Investment in savings for year 3 $ fill in the blank 33
Investment in savings for year 4 $ fill in the blank 34
Investment in savings for year 5 $ fill in the blank 35
Investment in savings for year 6 $ fill in the blank 36
Use the dual value 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. Round your answer to the nearest dollar.
$ fill in the blank 37
Use the dual value to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000. Round your answer to the nearest dollar.
Hoxworth should be willing to pay anything less than $ fill in the blank 38
.
Suppose that the annual payments are to be made at the end of 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. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Min F
s.t.
1) fill in the blank 39
F + fill in the blank 40
G1 + fill in the blank 41
G2 + fill in the blank 42
S1 = fill in the blank 43
2) fill in the blank 44
G1 + fill in the blank 45
G2 + fill in the blank 46
S1 + fill in the blank 47
S2 = fill in the blank 48
3) fill in the blank 49
G1 + fill in the blank 50
G2 + fill in the blank 51
S2 + fill in the blank 52
S3 = fill in the blank 53
4) fill in the blank 54
G1 + fill in the blank 55
G2 + fill in the blank 56
S3 + fill in the blank 57
S4 = fill in the blank 58
5) fill in the blank 59
G2 + fill in the blank 60
S4 + fill in the blank 61
S5 = fill in the blank 62
6) fill in the blank 63
S5 + fill in the blank 64
S6 = fill in the blank 65
7) fill in the blank 66
S6 + fill in the blank 67
S7 = fill in the blank 68
How much would Hoxworth save if this change could be negotiated? Round your answer to the nearest dollar.
$ fill in the blank 69