Posted by Kirsten on Thursday, December 1, 2011 at 8:44pm.
A farmer wishes to enclose a long rectangular pin that will then be divided into four separated, adjacent pins (all 4 pins are in a row) for different breeds of farm animals. He has 1100 feet of fencing available for use. What should the dimensions of the pin be so that he is able to maximize area? What is the maximum area?

Calculus  Reiny, Thursday, December 1, 2011 at 10:05pm
Let the width of each of the smaller pens be x, and let the length of each of the smaller pens be y
So the total of all fences = 8x + 5y
8x + 5y = 1100
y = 220  8x/5
Area = 4xy
= 4x(220  8x/5)
= 880x  32x^2/5
d(Area)/dx = 880  64x/5 = 0 for a max of area
64x/5 = 880
64x = 4400
x = 68.75
y = 220  8(68.5)/5 = 110
So each of the small pens should be 68.75 by 110
check my arithmetic
Answer This Question
Related Questions
 algebra  A farmer wishes to fence in 3 different breeds of animals in a ...
 Calculus  A ostrich farmer wants to enclose a rectangular area and then divide ...
 Calculus 2  A farmer wishes to build a fence for 6 adjacent rectangular pens. ...
 Precalculus  a farmer has available 1032 feet of fencing and wishes to enclose ...
 Math PLEASE  It's about arithmetic sequence . . (the sum) SOLUTION PLEASE THANK...
 Math PLEASE  It's about arithmetic sequence . . (the sum) SOLUTION PLEASE THANK...
 Maths  A manufacturer of cotter pin know that 5% of his product is defective. ...
 Precalculus  a farmer has available 1032 feet of fencing and wishes to enclose ...
 Precalculus  a farmer has available 1032 feet of fencing and wishes to enclose...
 Precalculus help fast  a farmer has available 1032 feet of fencing and wishes ...
More Related Questions