The manager of a financial firm is charged with managing the company’s cash flow. She must manage short term investments to maximize interest income, while making sure that funds are available to pay company expenses. She is considering three invest options over the next six months: A, a 1-month investment that pays 1.5% percent; B, a 3-month investment that pays 2.5%; and C, a 6-month CD that pays 5%. Assume the current month is month-1. The time horizon spans 1-7 months. For example, if you place a 6-mont CD in the first month, it will mature in the 7th month. The net expenses or income for the next six months are as follows: $48000, ($10000), $21000, ($18,000), $39000, ($11000). Values without brackets are expenses and values within brackets are incomes-incomes different from interest income. For example at the start of month 2, $14000 will be added to the company’s account. The company at the beginning of the first month has $280,000 in cash. At the end of the planning horizon (at node 7), you need to have a cash of minimum $30,000. If you believe that this cash at the end of the horizon is not achievable, you can even borrow money at the end of the planning period.
Draw a diagram to depict the flow of funds and formulate a linear programming model to the problem.