OPTIMIZATION

Problem: An open rectangular box is to be constructed by cutting square corners out of a piece of cardboard whose dimensions are given below and folding up the flaps. What dimensions will yield a box of maximum volume? Find the maximum volume. The length of the string is 54 cm.

Give the following:

• Representation, Illustration, Quantity to be Maximized or Minimized.
• Function, Computation of Derivative, Computation of Critical Numbers, Computation of Maximum Value
• Checking using Second Derivative Test
• Answer in Complete Sentence

Note: Please show the complete solution for everything. Thank you!