Step 1: Recall the function of each extruder zone.
Feed zone (R): closest to the hopper; its job is to receive and convey the pellets/powder. $\Rightarrow$ matches function 2.
Compression/transition zone (Q): solids bed compacts; viscous heating plus barrel heaters melt the polymer. $\Rightarrow$ matches function 3.
Metering zone (P): fully molten polymer is homogenized and delivered at a steady, nearly constant flow rate by the screw. $\Rightarrow$ matches function 4.
Working (mixing) zone (S): special mixing flights/pins/clearances impose high shear for effective mixing. $\Rightarrow$ matches function 1.
Step 2: Compile the mapping.
$P \to 4,\; Q \to 3,\; R \to 2,\; S \to 1$ which is option (A).
Final Answer:
\[
\boxed{\text{(A) } P\!-\!4,\; Q\!-\!3,\; R\!-\!2,\; S\!-\!1}
\]