Support Vector Machines $[6]$

The soft margin support vector machine solves the following optimization problem:

argmin$\frac{1}{2}||w|{|}^2+C{\displaystyle \underset{i}{\overset{?}{}}}{}_i,$ subject $to{c}_i(w*x_i-b)1-{}_i,1in.$

What does the second term minimize $($be precise!$)?[1]$ What is the purpose of C$?$

$[1]$Next$,$ add arrows to all examples in the figure below, whose ${}_i$ values are positive$---$the length of the arrow should correspond with the value to the respective ${}_i![2]$ Are examples with a positive ${}_i$ value always misclassified; give a reason for your answer! $[2]$

No answer given at the moment.