Consider the beam with the given loading when M$=480$ lb$/$ft

$.$

An illustration of a horizontal beam and the load distribution on it$.$In the illustration, the beam has a left end marked A and a right end marked D$.$ The support at a length of $4$ feet from end A is labeled B and the support at a length of $2$ feet from end B is labeled C$.$ B is moveable while C is fixed. The distance B C is $12$ feet. The load distribution forms a trapezium$-$like front comprising vertical arrows of decreasing size from A to D$.$ The torque at end A is $450$ l b per feet and the force acting at point D is w subscript naught. A clockwise arrow on the end A is labeled $44\mathrm{.}1$ k i p per feet.

Determine the corresponding reaction at C$.$

The reaction at C is

lb