You are constructing an open top box for your cat to sleep in$.$ The plush material for the square bottom of the box costs $$\frac{6}{f}{t}^2$ and the material for the sides costs $$\frac{2}{f}{t}^2.$ You need a box with volume $4f^3.$ Find the dimensions of the box that will minimize the cost.

The dimensions of the box that will minimize the cost are $$ feet. $($enter a comma separated list$)$ help.....................