a cylindrical metal container, open at the top, is to have a capacity of 100\pi \, { \textrm{in}}^{3}. the cost of material used for the bottom of the container is $0.25/{ \textrm{in}}^{2}, and the cost of the material used for the curved part is $0.15/{ \textrm{in}}^{2}. find the dimensions that will minimize the cost of the material, and find the minimum cost.