Calc
posted by katie .
A 100 inch piece of wire is divided into 2 pieces and each piece is bent into a square. How should this be done in order of minimize the sum of the areas of the 2 squares?
a) express the sum of the areas of the squares in terms of the lengths of x and y of the 2 pieces
b) what is the constraint equation relating x and y?
c) does this problem require optimization over anopen or closed interval?
d) solve the optimization problem

Let one piece to shape the first square be 4x, then let the other piece be 4y
4x + 4y = 100
x+y = 25
y = 25x
Sum of areas = x^2 + y^2
= x^2 + (25x)^2
= 2x^2  50x + 625
d(Sum of areas)/dx = 4x  50
= 0 for a max/min of the sum of the areas
4x = 50
x = 12.5
( I defined the length as 4x instead of x to avoid fractions)
Respond to this Question
Similar Questions

Calculus
A wire 4 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be … 
math problem
A piece of wire 24 cm long is cut into two pieces and each piece is bent to form a square . Find the lenght of each piece of wire in order to maximize the sum of the area of the two squares? 
calculus
A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area? 
Calculus!!!
A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area? 
Calculus
A piece of wire 40 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much of the wire should go to the square to minimize the total area enclosed by both figures? 
calculus help please
A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? 
Calculus Help Please Urgent!!!
A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? 
Calculus
A wire 7 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be … 
Calc 1
A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? 
Calculus 1
A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area?