Question

6. (15) A farmer wishes to enclose a 4000 square meter field and subdivide it into four rectangular plots of equal area with fences parallel to one of the sides. Use the derivative to calculate what the dimensions of the field should be in order to minimize the amount of fencing required.

Answer 1

briven Area = 4000 sqm. 4000 = lb -0. be Perimeter = sbt2U-P 16300, do) from d = 4000 .p=5b+8000 b To find the minimum dimensions, we need to find derivative pl-5-800 b² Now Pl_o 5.8000 800 -5 CS Scanned with CamScanner

b?- 8000 = 1600 6² = 1600 => b= I lo. breadth b won't be negative b=40m p" - 16000 63 At b=40, p" - 16000 6 4002 -0.25 >o. loral minimum. :. At b=4o we have whom b=40 substitute in Co. 100 I= 4ood yo . d = 10om, b=hom are the will minimize the amount of fencing required = 100 m CS Scanned with CamScanner