Optimization: Fence Problem 2

Author:
hpp3
Topic:
Area, Calculus, Perimeter
A farmer needs to enclose a field with a fence partitioned down the center. He has 15 meters of fencing material. Determine the dimensions of the field that will enclose the largest and smallest areas.
Instructions:
  • Drag the purple 'X' or use the 'Show Animation' and 'Stop Animation' Buttons to change the dimensions of the field.
  • Click the check box 'Show Area' to show or hide the calculated area.
Make a Prediction: Determine the dimensions of the field that will enclose the largest area. What shape is this field?
  • Check your predictions by changing the dimensions of the field until the calculated area is the greatest.
Make a Prediction: Determine the dimensions of the field that will enclose the smallest area. What shape is this field?
  • Check your predictions by changing the dimensions of the field until the calculated area is the smallest.
Elaboration:
  • What is the domain for this problem? That is, what are the possible values for the width of the field?
  • What is the range for this problem? That is, what are the possible values for the height of the field?
  • Write an equation for the amount of fence the farmer has (this is your constraint).
  • Write an equation for the area of the field (this is what your are maximizing or minimizing).