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.
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).