Optimization

1
Optimization

• Locate the optimizing adjective, a word such
  as largest, least, minimal, etc.
• The noun this adjective modifies will be your
  key word. Assign it a variable name, e.g. A.
• Write an equation for this key word A some
  stuff (usually involving at least two other
  letters, say x and y). This is your principal
  equation.
• Look for some other information in the problem
  that lets you write an equation using the other
  letters. This is your constraint equation.
  Write it down and solve for either x or y .
• Replace the value you solved for (say y) in the
  principal equation to get a function of one
  variable, A(x).
• Use calculus to find the max/min of A(x) Find
  A(x), set it equal to 0 and solve. If
  necessary, use the second derivative test to see
  if the critical point you found is a max or a
  min.
• Re-read the problem to see whether they want x,
  A(x), (x, y ) or e.g. the dimensions.