Question: A capital budgeting problem. Somebody receives an inheritance of $300,000 and wants to invest it for five years with the goal of ending up with the maximum amount of money. Each year she want to take out $20,000 for personal consumption. She can invest in five projects, or she may buy a five-year bond yielding a yearly dividend of 6 percent, or she may, each year, put her money into annual certificates of deposit and draw 5 percent interest on them. The investment projects are as follows: for one unit of participation in project 1, $1 should be disbursed at the beginning of year 1, $1 at the beginning of year 2 and, again, $1 at the beginning of year 3. After 3 years, the project starts to yield returns: $0.50 per unit of participation becomes available at the beginning of the fourth year and $0.60 at the beginning of year 5. The final return per unit of participation, which becomes available at the end of year 5, is quoted to be $2. The stream of outlays and returns (measured in $) for each of the five projects are reported below.
(a) Set up the appropriate primal linear programming problem.
(b) Derive the associated dual problem and give a meaningful economic interpretation to each of its components (objective function, constraints, dual variables).