Use the Lagrange Method to solve the constrained optimization problems associated to the following objective functions:
a. $f(x, y) = xy$
b. $g(x_1, x_2) = x_1(x_2 + 4)$
c. $h(k, l) = k - 3l - kl$
d. $z(x, y) = 7 - y - x^2$
Constraint
$2 = x + 2y$
$8 = x_1 + x_2$
$6 = k + l$
$0 = x + y$
For the same functions in (5), solve the constrained optimization problems using the Substitution Method. Use second order conditions to determine whether the solutions proposed maximize or minimize the objective functions.
