Problem $4$ Value Functions and the Design Space $(4$ points$)$

Continuing Problem $3,$ let us map the value functions to the design $($act$)$ space. The following equations

have been derived for the diving board, assuming that $($i$)$ the board is simply supported at one end, and $($ii$)$

the diver's weight and dynamic forces are applied to the very end of the board.

Maximum Bending Stress: $,=6**\frac{Fl}{b{t}^2}$

Stiffness: $k=\frac{1}{4}**\frac{Eb{t}^3}{l^3}$

Mass: $m=btl$

where,

$F=$ force exerted $by$ the diver $(pounds)$

$l=$ length $of$ the diving board $(in)$

$b=$ width $of$ the rectangular cross$-$section $of$ the diving board $(in)$

$t=$ thickness $of$ the rectangular cross$-$section $of$ the diving board $(in)$

$E=$ Young's modulus $of$ the material $(psi)$

$p=($