Answer
$25000$
Work Step by Step
The differential form can be evaluated as follows:
$dw=\dfrac{\partial w}{\partial p} dp +\dfrac{\partial w}{\partial q} dq+\dfrac{\partial w}{\partial r} dr+\dfrac{\partial w}{\partial s} ds$
Re-write as:
$dw=qrsdp+prsdq+pqsdr+pqrds$
Let us consider that $dp=dq=dr=ds=0.05$ since this is the maximum rounding difference.
$dw=(50)(50)(50)(0.05)+(50)(50)(50)(0.05)+(50)(50)(50)(0.05)+(50)(50)(50)(0.05)$
This gives: $dw=(4)(50)^3(0.05)=25000$
