Calculus Word Problem
posted by Henry .
A farmer wishes to build a fence for 6 adjacent rectangular pens. If there is 600 feet of fencing available, what are the dimensions of each pen that maximizes total pen area?
The image looks like this:
box box box
box box box
also:
If the interior fencing is $3.00 per foot and the perimeter is $5.00 per foot, what are the pen dimensions that minimize cost?

assume each pen encloses 200 square feet of area in the 2nd part sorry!

part 2:
if each pen has width x and height y
xy=200
6x+8y=600
you have no room to vary the dimensions. So, I assume the 600 feet of fencing does not apply to part 2. Accordingly,
xy=200
cost c = 5(3x+4y)+3(3x+4y)
= 24x+32y
= 24x+32(200/x)
dc/dx = 24  6400/x^2
= 8(3x^2800)/x^2
dc/dx = 0 when x = 20√(2/3)
so, the pens are 20√(2/3) by 10√(3/2) 
25'x25'
Respond to this Question
Similar Questions

AP Calculus AB
A farmer wants to create a rectangular pen, which will be divided into six separate sections, as shown in the accompanying diagram. If he has 600 feet of fencing to use, what outside dimensions will maximize the area of the pen? 
math
a farmer has enough fencing to build 40 feet of fence. He wishes to build a rectangular pen nest to his barn wall forming one side of the pen. What dimension should he make the pen so as to enclose the greatest possibility area? 
Math please help
A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them as much room as possible to run. What are the dimensions of the rectangular pen with the largest area? 
Geometry
A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and 115 feet of fencing for the remaining 3 sides. What dimensions will give her the maximum area for the pen? 
Calculus 2
A farmer wishes to build a fence for 6 adjacent rectangular pens. If there is 600 feet of fencing available, what are the dimensions of each pen that maximizes total pen area? 
Calculus Follow Up
A farmer wishes to build a fence for 6 adjacent rectangular pens. If there is 600 feet of fencing available, what are the dimensions of each pen that maximizes total pen area? 
calculus
Farmer Jones has 210 meters of fence. She wishes to construct a rectangular pen using the river as one side and dividing the pen into six separate rectangular pens as shown. What should the dimensions of the combined pens be to maximize … 
Calculus
Farmer Jones has 480 feet of fence. She wishes to construct a rectangular pen divided into five separate pens, with one of the pens twice as large as each of the other four (see figure). She must use part of her 480 feet of fencing … 
Algebra
Word Problems: 1. A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. If he needs no fence along the river, what are the dimensions of the field that he can fence with the largest … 
math
a. A rectangular pen is built with one side against a barn. 1200 m of fencing are used for the other three sides of the pen. What dimensions maximize the area of theâ€‹ pen?