A rectangular storage container with an open top is to have a volume of 10 meters cubed. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

My work:

The area of the base is given by:

The area of the sides is given by:

I know the cost per square meter so:

So the total cost is represented by:

And I know that the volume is equal to 10 cubic meters so:

I plug that into my cost formula:

Take the derivative:

I find the critical points to be 0, 1.44.

Then I find that the absolute minimum is 1.44 but when I use this number I get the incorrect answer of 124 (ish).

Any suggestions?