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	175	230	300	320	350	480

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 4.05% 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	$1025	6.25	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 1F	+	fill in the blank 2G1	+	fill in the blank 3G2	+	fill in the blank 4S1	=	fill in the blank 5
	fill in the blank 6G1	+	fill in the blank 7G2	+	fill in the blank 8S1	+	fill in the blank 9S2	=	fill in the blank 10
	fill in the blank 11G1	+	fill in the blank 12G2	+	fill in the blank 13S2	+	fill in the blank 14S3	=	fill in the blank 15
	fill in the blank 16G1	+	fill in the blank 17G2	+	fill in the blank 18S3	+	fill in the blank 19S4	=	fill in the blank 20
			fill in the blank 21G2	+	fill in the blank 22S4	+	fill in the blank 23S5	=	fill in the blank 24
					fill in the blank 25S5	+	fill in the blank 26S6	=	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 39F	+	fill in the blank 40G1	+	fill in the blank 41G2	+	fill in the blank 42S1	=	fill in the blank 43
2)	fill in the blank 44G1	+	fill in the blank 45G2	+	fill in the blank 46S1	+	fill in the blank 47S2	=	fill in the blank 48
3)	fill in the blank 49G1	+	fill in the blank 50G2	+	fill in the blank 51S2	+	fill in the blank 52S3	=	fill in the blank 53
4)	fill in the blank 54G1	+	fill in the blank 55G2	+	fill in the blank 56S3	+	fill in the blank 57S4	=	fill in the blank 58
5)			fill in the blank 59G2	+	fill in the blank 60S4	+	fill in the blank 61S5	=	fill in the blank 62
6)					fill in the blank 63S5	+	fill in the blank 64S6	=	fill in the blank 65
7)					fill in the blank 66S6	+	fill in the blank 67S7	=	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