5. Cash Flow Management.

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

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).

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.