Suppose that this beam needs to be designed such that its free end is capable of supporting a $180-lb$ person

with a $1\mathrm{.}5$ factor of safety $($i$.$e$.270$ lb maximum load$),$ with a maximum end deflection of $1$ inch. Suppose

also that we only have $2"$x$3"$ bar stock available, in both aluminum and steel. What length would need to

be cut from steel and aluminum bar stock to meet the criteria above?

Figure $1$: Cantilevered beam configuration.