**Question: ** A rectangular box with an open top is to have a volume of 10 cubic feet. The length of the base is twice its width. Material for the base costs $10 per square foot and for the sides costs $6 per square foot.

(a) (10 points) Find the dimensions that minimize the cost of the box.

(b) (5 points) How much does the cheapest box cost? (5 points) Which method described in the lecture are you using (endpoint method or first derivative test) and why?