Constrained Minimization Problem(HELP )

[MathNoob123]

Homework Statement

A closed rectangular box is made with two kinds of materials. The top and bottom are made with heavy-duty cardboard costing $0.36 per square foot, and the sides are made with lightweight cardboard costing $0.06 per square foot. Given that the box is to have a capacity of 162 cubic feet, what should its dimensions be if the cost is to be minimized?

Homework Equations

Surface Area A=2xy+2xz+2yz
Volume= V=xyz=162

partial derivitations are required to do this(which i know how to do)

The Attempt at a Solution

The hard part that I am trying to figure out is creating the Cost equation. All I need to know is what that equation would be and I can take care of everything afterwards. Like mentioned before in (2), the surface area A=2xy+2xz+2yz, but I have no idea how I am going to create a cost function including the prices mentioned in the problem. PLEASE HELP. BLESS ANYONE WHO DOES. THANK YOU SO MUCH IN ADVANCE!

 

[tiny-tim]

… The top and bottom are made with heavy-duty cardboard costing $0.36 per square foot, and the sides are made with lightweight cardboard costing $0.06 per square foot.
…
I have no idea how I am going to create a cost function including the prices mentioned in the problem.

Hi MathNoob123!

Multiply the area of heavy-duty cardboard by the cost per area, and multiply the area of lightweigh cardboard by the cost per area, and add

 

[MathNoob123]

Hi MathNoob123!

Multiply the area of heavy-duty cardboard by the cost per area, and multiply the area of lightweigh cardboard by the cost per area, and add

I have already solved the problem, but thank you very much for replying. Really appreciate it.