What are the dimensions of the cedar chest that minimize the cost?

[Majestic_]

Homework Statement

The length of a cedar chest is twice its width. The cost/dm^2 of the lid is four times the cost/dm^2 of the rest of the cedar chest. If the volume of the cedar chest is 1440 dm^3, find the dimensions so that the cost is a minimum.

Homework Equations

LWH = 1440
W = 2L

The Attempt at a Solution

I don't even know where to start. Can anyone help me get started? I've never seen a question like this in my examples, so I'm kind of lost.

 

[Robert1986]

Homework Statement

The length of a cedar chest is twice its width. The cost/dm^2 of the lid is four times the cost/dm^2 of the rest of the cedar chest. If the volume of the cedar chest is 1440 dm^3, find the dimensions so that the cost is a minimum.

Homework Equations

LWH = 1440
W = 2L

The Attempt at a Solution

I don't even know where to start. Can anyone help me get started? I've never seen a question like this in my examples, so I'm kind of lost.

So, you have enough information to be able to write a function for the cost of this trunk. Now, as the various dimensions change, the cost is going to change. You want to find the point at which the cost of the trunk is at a minimum. So, start by getting a function for the cost of the trunk in terms of just one variable. Then, report back if you have more questions.

 

[Majestic_]

So, you have enough information to be able to write a function for the cost of this trunk. Now, as the various dimensions change, the cost is going to change. You want to find the point at which the cost of the trunk is at a minimum. So, start by getting a function for the cost of the trunk in terms of just one variable. Then, report back if you have more questions.

I already knew this. I just don't know where to get started to finding the function that needs to be differentiated (I've never solved a question like this before nor seen one in any of my examples).

 

[Robert1986]

Oh, so is it finding the cost function that is giving you troubles?

I would start by assuming that the sides and the bottom of the trunk cost $1/dm^2, and that the lid costs $4/dm^2. Then, for example, the cost of the lid is $4 * l*w = $4 * 2w^2. So, you are going to want to get a function in w, then differentiate that one.