Design a section shape: A beam requires a rectangular cross section with a gross moment of

inertia $I_g$ of at least $25,000i{n}^4$ to limit deflections $(\{$:$Ig25,000i{n}^4).$ The self$-$weight of this

beam must be no more than $0\mathrm{.}40\frac{k}{f}t(W_{sw}0\mathrm{.}40\frac{k}{f}t)$ using normal weight concrete of $150$

pcf$.$ The beam width must be at least $10$ inches $(b{10}^{\text{'}\text{'}})$ and can be no taller than ${30}^{\text{'}\text{'}}"$

$30").$ Using only integer inch values for both dimensions, design a rectangular cross section that

meets all these criteria. $($Hint: There are $2$ correct answers, you are required to find one$)$

Simultaneously achieve these constraints:

Ig $25,000i{n}^4$

$W_{sw}0\mathrm{.}40\frac{k}{f}t($use $150pcf$ concrete$)$

Width $b10$ in $($integer values only$)$

Height $h30$ in $($integer values only$)$