$(50$ Points$)$ Problem $1$: A catheter produced for use in a medical device must meet exacting specs: $2\mathrm{.}45mm$

plus or minus $0\mathrm{.}05mm$ on its outside diameter $($OD$).$ The catheter is made via an extrusion process, which is

based on three factors: A$,$ extruder feed rate: $900-1,100g\frac{r}{h}r$; B$,$ zone$-1$ temperature, $165-195C$; and C$,$

raw material supplier: Acme $(-1)$ or Ecma $(+1).$ The RSM design chosen follows:

$($a$)$ In this design, you have a qualitative $($or categorical$)$ factor. How else could you approach this

design?

$($b$)$ What type of RSM design would the one shown above be$?$

$($c$)$ If the fitted model is

$Y=2\mathrm{.}407+0\mathrm{.}048A+0\mathrm{.}102B+0\mathrm{.}070C-0\mathrm{.}037A^2-0\mathrm{.}064B^2+0\mathrm{.}046AB-0\mathrm{.}016AC-0\mathrm{.}037BC$