Constrained Minimization Problem(HELP )

  • Thread starter Thread starter MathNoob123
  • Start date Start date
  • Tags Tags
    Minimization
MathNoob123
Messages
15
Reaction score
0

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!
 
Physics news on Phys.org
MathNoob123 said:
… 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! :wink:

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 :smile:
 
tiny-tim said:
Hi MathNoob123! :wink:

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 :smile:


I have already solved the problem, but thank you very much for replying. Really appreciate it.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top