A power company is considering how to increase its generating capacity to meet expected demand in its growing service area. Currently, the company has 740 megawatts (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 in Megawatts (MW)	780	860	950	1,040	1,180

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 (in thousands of dollars) of expanding the company's generating assets to the minimum required levels. (Let X_ij be the number of generators of type i purchased in year j where i = 1, 2, 3, 4 correspond to 10, 25, 50, and 100 MW generators, respectively.

(b) Implement model in a spreadsheet and solve it. What is the optimal solution?

Please use values that are given in the problem.