please answer with correct and detailed calculations and explanations. make sure supporting statements are also provided for each step and calculation:

Problem 9:' A manufacturer has identified the following options for obtaining a machined part: it can buy the part at $200 per unit (including materials); it can make the part on a numerically controlled semiautomatic lathe at $75 per unit (including materials); or it can make the part on a machining center at $15 per unit (including materials). There is negligible fixed cost if the item is purchased; a semiautomatic lathe costs $80000; and a machining center costs $200000. The total cost for each option is Purchase cost = $200 X Demand Produce using lathe cost = $80000 + $75 X Demand Produce using machining center cost = $200000 + $15 X Demand Find the break-even points