An electrical utility needs to generate $6,400$ 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.

A B C D E

Fixed start$-$up cost $$3,000$ $$2,000$ $$2,500$ $$1,500$ $$1,000$

Cost per megawatt$/$day generated $$5$ $$4$ $$6$ $$6$ $$7$

Maximum capacity $($MW$/$day $2,1001,8002,5001,5003,000$

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Formulate and solve this model on a spreadsheet.

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

Note: Leave no cells blank. Enter $"0"$ wherever required.

Determine the total cost.