Problem $2(20$ pts$)$ Zener Circuits

$($a$)$ Given the following circuit, what is the maximum and minimum input voltage that can be regulated? For this Zener diode, $V_z=12V$@$I_z=15mA,I_{zk}=0\mathrm{.}5mA,I_{zm}=30mA,$ and $Z_Z=8.$

$($b$)$ Given the circuit below, using a $1$N$4740$A Zener $($data sheet included$),$ determine

a$.$ the necessary value of the limiting resistor, $R_1,$ and

b$.$ the minimum load, $R_L,$ that can be driven by the Zener.