TeX source:

\begin{aligned}\text { Minimize } C &=2(\text { top area })+5(\text { bottom area })+3(\text { side area }) \\&=2\left(\pi r^{2}\right)+5\left(\pi r^{2}\right)+3(2 \pi r h)=7 \pi r^{2}+6 \pi r\left(\frac{100}{\pi r^{2}}\right)=7 \pi r^{2}+\frac{600}{r}\end{aligned}