What is the optimal volume of a box with given dimensions using calculus?

Click For Summary

Homework Help Overview

The discussion revolves around finding the optimal volume of a box given specific dimensions, utilizing calculus for maximization. Participants are attempting to clarify the setup and reasoning behind the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing the formulation of the volume equation based on the dimensions provided. There is confusion regarding the definition of variables and the correct expression for volume. Questions are raised about the meaning of the variable x and whether it accurately represents the dimensions being manipulated.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the formulation of the problem. Some guidance has been offered regarding the need to define variables and ensure the correct volume equation is used. Multiple interpretations of the problem setup are being explored.

Contextual Notes

Participants have noted issues with the clarity of the original problem statement due to handwriting and scanning quality. There is an emphasis on the need for clear definitions and explanations in the formulation of the problem.

Elihu5991
Messages
33
Reaction score
0

Homework Statement


SEE QUESTION IMAGE


Homework Equations


SEE ABOVE


The Attempt at a Solution


SEE WORKINGS IMAGE
 

Attachments

  • Scan 1.jpg
    Scan 1.jpg
    23.7 KB · Views: 392
  • Scan.jpeg
    Scan.jpeg
    13.4 KB · Views: 452
Physics news on Phys.org
Can you type in your work?

ehild
 
Sorry that my handwritiing is too messy and scan isn't done right. Just trying to get this done ASAP.

(25-2x)(40-2x)

y=(25-2x)(-2)+(40-2x)(-2)
=-50+4x-40+2x
=-90+6x
x=15

Not sure what to next do.
 
Elihu5991 said:
Sorry that my handwritiing is too messy and scan isn't done right. Just trying to get this done ASAP.

(25-2x)(40-2x)

y=(25-2x)(-2)+(40-2x)(-2)
=-50+4x-40+2x
=-90+6x
x=15

Not sure what to next do.

Is x the length of the corner pieces cut out? If so, you need to define it in words; a formulation without an explanation is worth 0.

Also, is (25-2x)*(40-2x) the thing you want to maximize? Why? What does the box look like if you use your proposed solution of x = 15?
 
Elihu5991 said:
Sorry that my handwritiing is too messy and scan isn't done right. Just trying to get this done ASAP.

(25-2x)(40-2x)

y=(25-2x)(-2)+(40-2x)(-2)
You mean y', not y.

Also, I'm guessing that you want to maximize the volume. If so, then
y = (25-2x)(40-2x)
as the volume equation would be wrong. You're missing the height. What would it be?
 

Similar threads

Maximizing Volume Formula for Given Box Dimensions and Cut Size
  • · Replies 1 ·
Replies
1
Views
2K
Optimization lagrangian problem
  • · Replies 1 ·
Replies
1
Views
1K
Derive the Volume of a Sphere using Calculus
  • · Replies 7 ·
Replies
7
Views
2K
Issue With Optimization Problem
  • · Replies 3 ·
Replies
3
Views
2K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K
Maximizing the volume of a cylinder
  • · Replies 1 ·
Replies
1
Views
2K
Volume of Revolution: Find V with Shell Method
  • · Replies 13 ·
Replies
13
Views
2K
Optimizing Cost per Unit with Calculus
  • · Replies 13 ·
Replies
13
Views
2K
Finding Volume and Surface Area of a Banana Using Calculus
  • · Replies 1 ·
Replies
1
Views
7K
Calculus II: Convergence of Series with Positive Terms
  • · Replies 3 ·
Replies
3
Views
2K