Consider the spring system shown in Figure $4$A$.$ The following information is

provided: the cantilever beam is $10$ feet long, has an E of $29000$ ksi, an A of $10$

in$2$ and an I of $2000$ in$4$; the beam has a stiffness to resist bending of $50$

kips$/$inch; the hanger is $5$ feet long, has an E of $1000000$ psi and is a rectangular

cross$-$section $1\mathrm{.}5$ inch wide by $3\mathrm{.}5$ inch deep; and the spring is known to require a

force of $120$ kips to make it stretch $3$ inches. Determine the equivalent spring

stiffness $($kip$/$inch$)$ of the entire system.