Problem $4(30$ pts$)$: Evaluation of Influence Lines. Consider the following beam with potential load a concentrated load equal to $100$ kN $.$ The load can be placed anywhere on the beam.

a$)$ What is the worst possible positive or negative moment at E created by the load?

b$)$ What is the worst possible shear $($in absolute value$)$ at B created by the load?

c$)$ What is the influence line for the shear at H $.$

d$)$ Where should a uniform distributed load of q$=30$kn$//$m $($with length of your choice$)$ should be placed to get the maximum positive shear at H$.$ Do not forget to also add the point load given on the drawing below in the right position on the beam as well.