Consider the following problem.
Maximize Z = 2x1 +5x2 +7x3,
Subject to
x1 + 2x2 + 3x3 = 6
and
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
(a) Graph the feasible region.
(b) Find the gradient of the objective function, and then find the projected gradient onto the feasible region.