A $20000m^3$ rectangular cistem is to be made from reinforced concrete such that the interior length will be twice the height. If the cost is $$\frac{40}{m^2}$ for the base, $$\frac{100}{m^2}$ for the side walls, and $$\frac{200}{m^2}$ for the roof, find the interior dimensions $($to one decimal place$)$ that will keep the cost to a minimum. To protect the water table, the building code specifies that no excavation can be more than $22m$ deep. It also specifies that all cistems must be at least $1m$ deep.