One Knob Left to Turn

A quality-control neuron on a production line reads three sensor measurements of each finished part and computes

$z = w_1x_1 + w_2x_2 + w_3x_3 + b$

Training has already set the weights, and they stay fixed:

$w_1 = 3, \qquad w_2 = -2, \qquad w_3 = 1$

A part is flagged for manual inspection when $z > 0$ . A value of exactly $z = 0$ is not flagged.

Here is the latest batch:

part	$x_1$	$x_2$	$x_3$
P1	$2$	$1$	$0$
P2	$1$	$3$	$2$
P3	$0$	$-2$	$1$
P4	$3$	$2$	$-2$
P5	$1$	$0$	$6$

The inspector has time to examine only two parts from this batch, so the bias $b$ is to be chosen so that exactly two of the five are flagged.

What is the largest value of $b$ for which exactly two parts are flagged?

Give the exact value.