A financial manager is managing a cash fund. His investment alternatives available are various certificates of deposit, also known as CDs, as listed in the following table:

Investment Yield Availability

1-month CD 0.5% Beginning of each month

3-month CD 1.75% Beginning of Months 1, 2, 3, 4

6-month CD 2.3% Beginning of Month 1

However, he also must ensure that sufficient funds are available to pay company expen- ditures over the next six months. The following table lists the net expenditures (in thou- sands of dollars) that the manager is obligated to cover (cash amounts in parenthesis indicate a net inflow of cash rather than outflow).

Month Net Expenditures ($1,000s)

1 $45

2 ($11)

3 $25

4 ($22)

5 $43

6 ($15)

The cash on hand to invest at the start of month 1 is $200,000 and the minimum cash required to be available at the end of month 6 is $100,000. Develop and solve a linear program that will recommend how to invest to maximize the amount of interest income accrued over the next six months while satisfying all financial commitments.

(Hint: Investment time starts at the beginning of the month and returns at the end of the month. For example, money invested in a 1-month CD in month 1 will be invested at the beginning of month 1 and returned with interest at the end of month 1. Likewise, money invested in a 3-month CD at the start of month 1 will be returned with interest at the end of month 3.)