A power company is considering how to increase its generating capacity to meet expected demand in its growing service area. Currently, the company has 750 mega- watts (MW) of generating capacity but projects it will need the following minimum generating capacities in each of the next five years: Year 1 2 3 4 5 Minimum Capacity 780 860 950 1060 1180 in Megawatts (MW) The company can increase its generating capacity by purchasing four different types of generators: 10 MW, 25 MW, 50 MW, and/or 100 MW. The cost of acquiring and installing each of the four types of generators in each of the next five years is summarized in the following table: Generator Size Cost of Generator (in $1,000s) in Year 1 2 3 4 5 10 MW $300 $250 $200 $170 $145 25 MW $460 $375 $350 $280 $235 50 MW $670 $558 $465 $380 $320 100 MW $950 $790 $670 $550 $460 a. Formulate a mathematical programming model to determine the least costly way of expanding the company's generating assets to the minimum required levels. b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution?