(Solved): We are given that there is 19,200cm2 of materhal avalable to make the box. Therefore, 5=19,200. W ...

We are given that there is $19,200{\mathrm{cm}}^2$ of materhal avalable to make the box. Therefore, $5=19,200$. We substitute this value inte the surface area equabion determined in the previlous step $\begin{array}{rl}s& =b^2+4hb\\ 19,200& =b^7+4hb\end{array}$ We then solve the resubing equation for $h$. $\begin{array}{c}19,200=b^2+4hb\\ h=\end{array}$ Then we substinte this expression for b into the volume cquation determined in the crevious step and simpiry the rewit. $\begin{array}{l}v=b^{2}h\\ v=4,800b-(\end{array}$ Recaling chat volume and the length of the base must be greater 0 , we note that tres equation is valia when $0<b<()\sqrt{3}$.