February 21, 2017

Homework Help: Calculus

Posted by Jill on Sunday, January 16, 2011 at 2:03pm.

Here is the problem I am working on:

Romeo is commissioning the construction of a four-inch-tall box made of precious metals to give to his bride, Juliet. The jewelry box will have rectangular sides, a bottom and a top.
The longer sides and the top will be made of gold, at $300/in^2.
The shorter sides will be made of platinum, at $550/in^2.
The bottom will be made of plywood, at $0.02/in^2.
What dimensions will provide Romeo with the lowest cost if he is adamant that the box have a volume of 50 in^3?

I am aware that this involves minimizing the cost, and thus taking the derivative of a cost function for the situation. Can anyone tell me what the cost function for this would be?

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