$(40$ points$)$

a$)$ Design an inverting$-$ summing amplifier using a $120$

k$$k$$

resistor in the feedback path so that$$

vo$=(8$va$+5$vb$+12$vc$)$vo$=8$va$+5$vb$+12$vc

$$

Use

$$

$15$V power supplies.$$

$$

$$

$$

b$)$ Suppose

va$=2$Vva$=2$V

and

vc$=1$Vvc$=1$V

$.$ What range of value for

vbvb

will keep the op amp in its linear operating region?$$