Calculus - optimization problem

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Homework Help Overview

The discussion revolves around an optimization problem in calculus involving an aquarium's dimensions and cost minimization. The original poster presents a cost function based on the dimensions of the aquarium and its volume constraint.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the volume and cost functions, with the original poster expressing difficulty in deriving a usable equation. Some suggest using the volume formula to express one variable in terms of another, while others question the appropriateness of using Lagrange multipliers for this problem.

Discussion Status

The conversation is ongoing, with participants exploring different methods to derive necessary equations. The original poster has attempted to express height in terms of width and length but encounters inconsistencies, leading to confusion about the feasibility of the dimensions. There is no explicit consensus on the best approach yet.

Contextual Notes

There is a noted constraint regarding the use of Lagrange multipliers, as the original poster has been advised against it for this specific problem. Additionally, the original poster expresses uncertainty about missing equations necessary for solving the problem.

Pearce_09
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ok, i have an aquarium of volume V... where the cost of the base is 5 times of the sides... let h- height , w- width, l - lenght...
therefore 2hw + 2hl is the cost of the sides and 5wl is the cost of the base
therefore
total cost = 2hw + 2hl + 5wl --> min
and i want find the dimensions to minimize cost.
I know how to do problems like these I've done many, its just this one is somehow bothering me...
i need to solve for 1 variable then i have a formula with 2 variables.. then i take the partial derivatives to see if my dimensions that i find indeed minimize cost. but for some reason i can't even get past my total cost formula... help please
 
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You know the volume formula, so that in conjunction with your cost forumula will provide you with one variable in terms of another and bingo
 
V= whl is one equation. Can you use the "lagrange multiplier" method?
 
i know how to use lagrange.. but i was told not to for this question
 
I use my cost equation to solve for h and got
h = -5wl / 2w + 2l
and when i sub that into volume and partial derive but it doesn't make any sense.. I get l = w and then that implies that h = -10/8 ... not possible to have a negative number
 
No, you don't have a cost equation. You only have a cost function that you want to minimize. You don't know what it is equal to. (It certainly isn't equal to 0!) The only equation you have is V= whl
 
im missing an equation then, which I am having trouble finding...
 
I just don't understand how to find this other equation
 

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