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 megawatts (MW) of generating capacity but projects that it will need the following minimum generating capacities in each of the next five years:

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:

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 optimalsolution?

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Year 2 3 4 5 Minimum Capacity 780 809501060 1180 in Megawatts (MW) Cost of Generator (in $1,000s) in Year Generator Size 10 MW 25 MW 50 MW 100 MW 2 3 4 $300 $250 $200 $170 $145 $460 $375 $35080 %235 $670$558 $465 380$320 $950 $790 $670 $550 $460