A rectangular storage container with an open top is to have a volume of 10 $m^3$. The length of its base is twice the width. Material for the base costs $9 per $m^2$. Material for the sides costs $9.6 per $m^2$. Find the dimensions of the container which will minimize cost and the minimum cost.

base length = m

base width = m

height = m

minimum cost = $