Exercise 3.3 Biasing a crappy FM transmitter circuit

BC546s can be obtained in A, B or C-grade, with as main difference the current gain:

• ${\mathit{\beta fe}}_A=100$
• ${\mathit{\beta fe}}_B=250$
• ${\mathit{\beta fe}}_C=800$

The circuit schematic below — of a crappy FM transmitter [2] — does not indicate whether the BC547 should be type A, B or C, so the current gain of this transistor is very uncertain. This leads to an uncertain collector current $I_C$ and consequently uncertain voltage across the $1k\mathrm{\Omega }$ resistor in the circuit schematic. For proper operation of the BC547, its $V_{\mathit{CE}}$ must be larger than about 100mV and $V_{\mathit{CE}}$ should not be very close to $V_{\mathit{CC}}$. Calculate whether this is the case for all types (A,B,C) of the BC547.