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 $123456$

Payment $190215240285315460$

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 $4\%$ 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

$1$ $$10556\mathrm{.}7503$

$2$ $$10005\mathrm{.}1254$

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.

$62345\_09\_$ch$09\_$p$358-418.$qxd $12/22/115$:$57$ PM Page $396$

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.$

d$.$ Suppose that the annual payments are to be made at the end of each year. Reformulate

the model to accommodate this change. How much would Hoxworth save if this

change could be negotiated?