What are the dimensions of a parcel with 2322m3 volume and minimal string usage?

Click For Summary
SUMMARY

The discussion focuses on optimizing the dimensions of a rectangular parcel with square ends to minimize the string length used while maintaining a volume of 2322m³. The volume is expressed as V = lwh, where l is the length, w is the width, and h is the height. The dimensions function is defined as D = 2l + 2h + 4w. The challenge arises from having three variables, making it difficult to express D in terms of a single variable for minimization.

PREREQUISITES
  • Understanding of volume calculations for rectangular prisms
  • Familiarity with optimization techniques in calculus
  • Knowledge of functions and their derivatives
  • Basic algebra for manipulating equations
NEXT STEPS
  • Explore optimization techniques using calculus for multivariable functions
  • Research methods for solving systems of equations with three variables
  • Learn about geometric properties of rectangular prisms and their implications on volume
  • Investigate the application of Lagrange multipliers in constrained optimization problems
USEFUL FOR

Mathematicians, engineering students, and anyone involved in optimization problems related to geometry and volume calculations.

Procrastinate
Messages
155
Reaction score
0
A rectangular parcel with square ends is tied up with string, which passes once around the parcel lengthwise and once crosswise. If the volume of the parcel is 2322m3, find its dimensions if the length of string used to tie it is to be minimised.

V = lwh = 2322

Let D be the dimensions function

D = 2l + 2h + 4w

I am a bit stuck here now because there are three variables and I can't use simultaneous equations to then make D with respect to l or h or w.

Did I interpret the question wrong?
 
Physics news on Phys.org
"A rectangular parcel with square ends" ...
 

Similar threads

Optimization word problem - minimizing surface area to find least expensive tank
  • · Replies 1 ·
Replies
1
Views
5K
What dimensions minimize the surface area of a box with a fixed volume?
  • · Replies 3 ·
Replies
3
Views
20K
Solving the Pup Tent Problem: Volume & Cost Minimization
  • · Replies 1 ·
Replies
1
Views
4K
C/C++ How to Solve Bisection C++ Problem for Calculating Volume
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Max and Min Problems: Solving with Calculus | Need Help & Explanation
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Solve Volume and Surface Area for Rectangular Open-Top Box: Apps of Cubics
  • · Replies 1 ·
Replies
1
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 230)
  • · Replies 1 ·
Replies
1
Views
3K
Mathematica This Week's Finds in Mathematical Physics (Week 230)
  • · Replies 1 ·
Replies
1
Views
4K