Public Service Indiana (PSI) is considering five possible locations to build power plants during the next 20 years. It will cost c i dollars to build a plant at site i and h i dollars to operate a...

Public Service Indiana (PSI) is considering five possible locations to build power plants during the next 20 years. It will cost c_i dollars to build a plant at site i and h_i dollars to operate a site i plant for a year. A plant at site i can supply k_i kilowatthours (kwh) of generating capacity. During year t, d_t kwh of generating capacity are required. Suppose that at most one plant can be built during a year, and if it is decided to build a plant at site i during year t, then the site i plant can be used to meet the year t (and later) generating requirements. Initially, PSI has 500,000 kwh of generating capacity available.

Formulate a recursion that PSI could use to minimize the sum of building and operating costs during the next 20 years.