mechanical subcontractor wants to buy an electric generator to power his equipment rather than use electricity from the local power company. After searching the market, he found $2$ options that had a fair price, either to buy a brand new Honda Dayton $5$KWh Electric Generator or rent it directly from the store. Furthermore, he had the option to rent the generator with the bonus of free gas for a year either per day, per week or per month. The price of the new generator was $$1,719$ and it consumes $$1\mathrm{.}49/$per hour for gas. He expects to use the generator $8$ hours per day and $5$ days a week. The daily rent is $$56\mathrm{.}5,$ the weekly rent is $$170$ and the monthly rent is $$510.$ The local power company is willing to provide him with power for $40$ cents$/$KW and a fixed fee of $$10/$month plus $5\%$ of the total for taxes for the duration of the project.

$1)$ Draw the break$-$even graph.

$2)$

Calculate the break$-$even points. How much time should the subcontractor use the generator

to make his investment profitable?

$3)$ What should the subcontractor do if he needs electricity for a project that will last for $18$ months