The beam shown below is used to support a dead load of 400 Ib/ft, a live load of 2 k/ft, and a concentrated load of 8 k. Derive (1) the influence lines for vertical reaction at A and moment at C. Then, determine (2) the maximum positive (Upward) vertical reaction at A, and (3) maximum negative moment (i.e, counterclockwise) at C. Assume A is a roller, C is fixed, and B is pinned.