MyOpenMath (Optimization)

Question

Linda and Casey wants to raise cows in a rectangular field with five internal partitions as shown. If the area of the field must be  square feet, what dimensions will require the least fencing?

The width should be_______  feet and the length should be_________ feet. (Round your answers to two decimal places)

Answer 1

Let x: length of field ; y: width (the 5 partitions will each be y feet)

xy = 12,400

y = 12,400 / x

Total fencing = 2x + 7y = 2x + 86,800 / x

f^'(x) = 2 - 86,800 / x² = 0

x² = 43,400

x = √43,400 ; y = 12,400 / √43,400