ABSTRACT
This chapter tells what an optimization problem is. It defines key terms that will be used throughout the book, including solution, constraint, feasible, objective function and optimal solution. A typical first-year calculus problem asks for the dimensions of a rectangle with a perimeter of 100 feet that has maximum area. Not all optimization problems have optimal solutions. This can happen in several ways. First, some problems are infeasible. Second, some problems are unbounded. Third, a feasible problem that is not unbounded can still fail to have an optimal solution, because feasible solutions might have values arbitrarily close, but never equal, to some value. The chapter defines duality and applies it to multivariate differential calculus, Sudoku puzzles, and matrices. It depicts a different way to explain why the square maximizes area.
