As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the annual payments (in thousands of dollars) shown in Table 1. The annual payments must be made at the end 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 and two government securities shown in Table 2. All three are availible to invest at the beginning of every year. During the first 3 years (i.e., Year 1, Year 2 and Year 3), a) the average risk index of invested funds cannot exceed 2.5; b) the average years to maturity at the beginning of each year cannot exceed 3. There are no risk or liquidity requirements for Years 4 to 6.

Solve this LP to minimize the initial amount needed at the beginning of Year 1.