Optimization help: minimizing cost of container

[dvdman2k]

I'm having some trouble with this problem. Every time I try it I reach a certain point and then it's like I hit a brick wall of sorts.

A rectangular storage container with an open top is to have a volume of 15 cm^3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

 

[skeeter]

A rectangular storage container with an open top is to have a volume of 15 cm^3

LWH = 15

The length of its base is twice the width.

L = 2W

so ... (2W)WH = 15

2W²H = 15

H = 15/(2W²)

Material for the base costs $15 per square meter.

base cost = 15(LW) = 15(2W*W) = 30W²

Material for the sides costs $6 per square meter.

two sides of area LH ... cost = 6*2*LH = 12(2W)[15/(2W²)] = 180/W

two sides of area WH ... cost = 6*2*WH = 12(W)[15/(2W²)] = 90/W

so, total cost is ...

C = 30W² + 180/W + 90/W

C = 30W² + 270/W = 30(W² + 9/W)

find dC/dW and find the value of W that minimizes the cost, then determine L, H, and the minimum cost.