1. Consider the following linearly constrained convex programming problem: f(x) = 32x - x + 50x - 10x + x-x2, Maximize subject to 3x + x 11 2x + 5x 16 X 0, X 0. Ignore the constraints and solve the resulting two one-variable unconstrained optimization problems. Use calculus to solve the problem involving x, and use the bisection method with = 0.1 and initial bounds 0 and 2 to solve the problem involving x. Show that the resulting solution for (x, x) satisfies all of the constraints, so it is actually optimal for the original