An electrical utility needs to generate $6,500$ megawatts of electricity today. It has five generators $($A$,$ B$,$ C$,$ D$,$ and E$).$ If any electricity is generated by a given generator, that generator must be started up and a fixed start$-$up cost is incurred. There is an additional cost for each megawatt generated by a generator. These costs, as well as the maximum capacity of each generator, are shown in the following table.

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Formulate and solve this model on a spreadsheet.

a$.$ Determine the minimum cost plan that meets the electrical needs for today.

Note: Leave no cells blank. Enter $"$O$"$ wherever required.

b$.$ Determine the total cost.