Find the solution of the objective function for problems (a) - (b) below. For each problem,
confirm that the optimum satisfies the Kuhn-Tucker conditions. At each solution, describe
whether the constraint(s) is binding.
a) Minimize the function[tex]c = 5x^{2} - 80x + y^{2} - 32y[/tex] subject to the constraints [tex]x,y\geq 0[/tex] and
[tex]x+y\geq 20[/tex]
b) Maximize the profit function [tex]\pi = 50x +10y[/tex] subject to the constraints [tex]x,y \geq 0[/tex] and [tex]x-y\leq 3[/tex] and [tex]5x+2y\leq \leq 20[/tex]
