$1.$ A laboratory is using micro$-$electrodes, which can be made in the laboratory or purchased. The equipment to produce the electrodes would cost $$800\mathrm{.}00.$ The research technician could manufacture the electrodes and is paid $$12\mathrm{.}00$ an hour. A research assistant could be trained to produce the electrodes and is paid only $$6\mathrm{.}80$ an hour. However, the assistant would require $2$ weeks of training, during which time the electrodes would have to be bought from an outside source. The cost of purchasing the electrodes is $$25\mathrm{.}00$ per piece, and every week they need $40$ electrodes. The technician could produce $10$ electrodes a day, as could the assistant after proper training. The material cost for each electrode is $$4\mathrm{.}00.$

$($a$)$ Determine the equations to represent the total cost $($Y$)$ for each of the three make$-$and$-$buy alternatives, in terms of the number of units $($x$).$ Draw the line for these equations on a single graph using Excel.