Problem $3-(15$ points$)$

Mamfacturing can be a consideration when looking for an "optimal" design due to the "economy of scale" which we will explore here. Different manufacturing processes will have varying design constraints and will cost different amounts. In general, there are start$-$up costs, $C_s,$ and running costs, $C_r.$ Start$-$up costs have to$-$be paid once per batch while running costs have to be paid for every part made.

$($a$)(5$ points$)$ Suppose that you are designing a product that will only ever be made in batches of $100$ units. What is the cost per unit if $CNC$ milling is used $)=($$$100,C_r$$$100$ verses injection molding: $)=($$$0\mathrm{.}75?($IInt: The unit cost for injection molding is $C_{\text{m}\text{o}\text{l}\text{d}}=$$$250\mathrm{.}75)$