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$).$

$\backslash$table$[[$Year$,1,2,3,4,5,6],[$Payment$,190,215,240,285,315,460]]$

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.

$\backslash$table$[[$Security$,$Current Price,Rate $(\%),\backslash$table$[[$Years to$],[$Maturity$]]],[1,$$$1055,6\mathrm{.}750,3],[2,$$$1000,5\mathrm{.}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.

a$.$ Use linear programming to find the minimum cash settlement necessary to fund the annual payments.