$(40$ points$)$ A plastic part can be $3$D printed for $$\frac{2}{?}$ part on a $3D$ printer that costs $$5,000.$ It can also

be injected molded for $$\frac{0\mathrm{.}05}{?}$ part with a custom$-$built injection molding system that costs $$50,000.$

$($a$)$ What is the breakeven point $($in terms of number of parts$)$ at which it saves money to use

injection molding instead of $3$D printing to make the parts.

$($b$)$ How much does it cost to make $100,000$ parts with each method $($including the cost of buying

equipment$)?$