QuestionAs part of his sinister plan, Dr. Evil decides to mail Mini-Me to Austin Powers, in order to conduct his dirty work. The box to be used for shipment must be a rectangular storage container with a volume of $10 \mathrm{ft}^{3}$. The top and bottom of the box will be square, but the sides will be somewhat longer. In addition, a different material will be used for the top and bottom. Dr. Evil has invented a breathable cardboard that costs $\$ 5$ per square foot (the regular cardboard sides cost only $\$ 2$ per square foot). Design a container for Mini-Me that will meet the volume requirements while minimizing the cost. Unfortunately, Dr. Evil's henchmen (who will eventually build the box) can only measure within half a foot. Rounding your dimensions to the nearest half-foot, what is the volume of the new box and how much will it cost to build?