a$)$ A silicon transistor is shown below with a minimum value of $=30.$ Given $V_{BE}$ sat $=0\mathrm{.}8V,V_{C{E}_{\text{s}\text{a}\text{t}}}=0\mathrm{.}2V,V_{B{E}_{\text{a}\text{c}\text{t}\text{i}\text{v}\text{e}}}=0\mathrm{.}7V$

i$)$Determine whether the transistor is in cutoff, saturation, or active region.

ii$)$If the $15$ K transistor is replaced with another resistance R$1,$ find the minimum value of R$1$ for which the transistor remains in the active region. $[$Consider $V_{BC}0\mathrm{.}5V$ for the active region$]$