Consider the following linearly constrained convex programming problem:

Maximize f(x)
32x1  50x2  10x2 2  x2 3  x1 4  x2 4

, subject to 3x1  x2 11 2x1  5x2 16 and x1 0, x2 0.

Ignore the constraints and solve the resulting two one-variable unconstrained optimization problems. Use calculus to solve the problem involving x1 and use the bisection method with 
0.001 and initial bounds 0 and 4 to solve the problem involving x2. Show that the resulting solution for (x1, x2) satisfies all of the constraints, so it is actually optimal for the original problem.