Question: Consider the following linear programming problem:
(a) Plot the constraints and determine the feasible set.
(b) Graph the gradient of the objective function and use the graphical solution technique to determine the optimal point. Compute the exact coordinates of the optimal point and its value of the objective function.
(c) Consider a second objective function Max z2 = 2x1 - x2. Ignoring the first objective, what is the optimal point? Compute its exact coordinates and its value of the objective function.
(d) Determine the nondominated frontier given the two objectives.
(e) Use the two objectives above to construct the composite objective function with weights w1 = ¾ and w2 = ¼. What is the optimal solution with this objective?