This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = xy; 4x² + y² = 8 maximum value minimum value

A company that makes and sells baseball caps has found that the total monthly cost C in dollars of producing x caps is given by the function C(x)=0.2x280x+9000. Find the production level that will minimize the monthly cost and find the minimum cost.

Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.