OPG has scheduled the construction of three new electrical generating plants 5, 10 and 15 years from now to meet growing demand in the eastern Ontario region. In order to have the funds available when the plants are constructed, funds need to be invested now to meet these future requirements. OPG has identified three assets that meet its risk requirements, each of which costs one million dollars per unit and offers the income streams as shown below (in millions of dollars). (For example, one million put into asset one today will yield 2 million in year five, 500 thousand in year 10 and nothing in year 15.) The table also includes the future cash estimates (in millions of dollars) for the construction of the new plants. Fractional units of these assets may be purchased.

Determine the least amount that OPG needs to invest today and how that investment should be allocated among the three assets. Any extra cash received in a given year beyond the requirements for the new plants will be used elsewhere and cannot be reallocated to another year.

1. Formulate a linear model. Give clear definitions to your decision variables.

2. Set up a spreadsheet model. Use Solver to find the optimal solution.

Year Asset 1 Asset 2 Asset 3 Cash flow required 5 2 1 0.5 400 10 0.5 0.5 1 100 15 0 1.5 2 300 U