Hewlitt Corporation established an early retirement program as part of its corporate restructuring. At the close of the voluntary sign-up period, 68 employees had elected early retirement. As a result of these early retirements, the company incurs the following obligations over the next eight years:

Year 1 2 3 4 5 6 7 8
Cash required 430 210 222 231 240 195 225 255

The cash requirements (in thousands of dollars) are due at the beginning of each year.

The corporate treasurer must determine how much money must be set aside today to meet the eight yearly financial obligations as they come due. The financing plan for the retirement program includes investments in government bonds as well as savings. The investments in government bonds are limited to three choices:

Bond Price Rate (%) Years to Maturity

1 $1150 8.875 5
2 1000 5.500 6
3 1350 11.750 7

The government bonds have a par value of $1000, which means that even with different prices each bond pays $1000 at maturity. The rates shown are based on the par value. For purposes of planning, the treasurer assumed that any funds not invested in bonds will be placed in savings and earn interest at an annual rate of 4%.

a. write an LP to minimize the funds that Hewlitt must invest today in order that they can meet their yearly obligations.

b. what is the minimum amount of funds needed, and how much is invested in bond 1, bond 2, bond 3, and how much is put in savings each year.