An electric utility is considering 5 possible locations to build additional power plants over the next 20 years. The cost of building a plant at each site, the annual operating cost and the energy/year that can be provided at each site are given, as well as the total energy requirement for each year of the planning horizon. Assume that at most one plant can be placed into service in a given year, and that it can produce its full energy contribution starting the year it is placed in service. The company can currently generate 500,000 kwh/year, using its existing resources. Develop the mathematical formulation for a dynamic programming model to determine the expansion plan that will minimize overall construction and operating costs over the 20 years.