A $10-$m beam is simply supported; a moving wheel load of $30$ kN is imposed. Using the concept of influence line. Determine the following:

$($a$)$ maximum reaction at the left support;

$($b$)$ maximum positive shear at a point $2$ m from the left support;

$($c$)$ maximum negative shear at a point $2$ m from the left support;

$($d$)$ the maximum positive moment at the mid span.