Posted by Lisa on Tuesday, January 3, 2012 at 10:17pm.
Could you please explain this problem step by step, thank you!
You are planning to make an open rectangular box that will hold a volume of 50 cubed feet. What are the dimensions of the box with minimum surface area?
- Calculus I Quick Optimization Problem - drwls, Tuesday, January 3, 2012 at 11:14pm
For symmetry reasons, the optimum must have a square base. Let the height of the walls be x and the side length be y
Volume = x^2*y = 50
Area = x^2 +4xy = x^2 + 4x*50/x^2
= x^2 + 200/x
dA/dx = 0 = 2x -200/x^2
x^3 = 100
x = 4.64 ft
y = 2.32 ft
- Calculus I Quick Optimization Problem - Damon, Tuesday, January 3, 2012 at 11:22pm
x = length
y = width
h = height
x y h = 50
area bottom = x y
area sides = 2 x h + 2 y h
total area a = x y + 2 x h + 2 y h
h = 50/xy
a = x y + 100/y + 100/x
da/dx=x dy/dx+y-100 dy/dx /y^2-100/x^2
for min = 0
dy/dx(x-100/y^2) + y-100/x^2 = 0
x y^2 = 100 and y x^2 = 100
y (100^2/y^4) = 100
y^3 = 100
y = 4.64
x = 100/y^2 = 4.64
h = 2.32
Answer This Question
More Related Questions
- calculus optimization problem - by cutting away identical squares from each ...
- Calculus-Applied Optimization Problem - If a total of 1900 square centimeters of...
- Calculus - Given: available material= 1200cm^2 Box w/ square base & open top ...
- Calculus - A rectangular tank with a square? base, an open? top, and a volume of...
- optimal dimensions - Applications of derivatives You are planning to make an ...
- Calculus - I actually have two questions: 4. An open box is to be made from a ...
- Calulus/Optimization - I don't understand how to solve optimization problems, (...
- Calculus- PLEASE HELP - A rectangular piece of tin has an area of 1334 square ...
- Calculus - What is the smallest possible slope for a tangent to y=x^3 - 3x^2 + ...
- Calculus 1-Optimization - A box with a square base and open top must have a ...