Problem 1 of 5
Maximize

A farmer has 100 meters of fencing to enclose a rectangular field. What dimensions x and y give the largest possible area?

First, which quantity does this problem ask you to maximize? (The other two are not what you optimize.)

The optimization setup checklist
  1. 1.Draw and label a picture.
  2. 2.Name the variables.
  3. 3.Write the objective (what you optimize).
  4. 4.Write the constraint (what is fixed).
  5. 5.Substitute to get the objective in one variable.
  6. 6.State the domain, endpoints included.
  7. 7.Differentiate and find the critical points.
  8. 8.Run a derivative test, then answer the actual question with units.

Optimization Setup Builder: Objective vs Constraint from CalcLearn, free AP Calculus study tools.