# Question

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.

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.

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