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 one-dimensional search procedure 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.