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
185
225
290
310
360
450
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 4.25% 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
$1035
6.75
3
2
$1000
5.425
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.
F
+
G1
+
G2
+
S1
=
G1
+
G2
+
S1
+
S2
=
G1
+
G2
+
S2
+
S3
=
G1
+
G2
+
S3
+
S4
=
G2
+
S4
+
S5
=
S5
+
S6
=
Round your answer to the nearest dollar. If an amount is zero,
enter "0".
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
$
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.
$
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
$ .
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)
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 much would Hoxworth save if this change could be negotiated?
Round your answer to the nearest dollar.
$