A beam is depicted as shown below, where points A and C are assumed to be roller supports, point D is assumed to be a hinge support, and point B is assumed to be an internal pin connection. The beam is subjected to three types of loads: a $1\mathrm{.}2$ kN$/$m uniformly distributed live load, a $0\mathrm{.}5$ kN$/$m uniformly distributed dead load, and a $40$ kN point load.$($a$)$ Determine the influence lines for shear force and bending moment at point E$.($b$)$ Determine the maximum possible positive shear force at point E under the combined action of the three loads.$($c$)$ Determine the maximum possible positive bending moment at point E under the combined action of the three loads.