Question: 3. (30 points) Consider the linear optimization problem (a) (10 points) Solve this problem graphically. Show that the set of optimal solutions is unbounded. What

3. (30 points) Consider the linear optimization

3. (30 points) Consider the linear optimization problem (a) (10 points) Solve this problem graphically. Show that the set of optimal solutions is unbounded. What is the optimal value? (b) (5 points) Perform one simplex pivot starting from the basic feasible solution x=(4,0,6,0). Show that the resulting basic feasible solution is optimal. (c) (10 points) Use the updated tableau to find a feasible solution x and a direction dR4 so that the set of optimal solutions can be written S={xR4:x=x+tdfort0}. (d) (5 points) Give an optimal solution with x2=2. 3. (30 points) Consider the linear optimization problem (a) (10 points) Solve this problem graphically. Show that the set of optimal solutions is unbounded. What is the optimal value? (b) (5 points) Perform one simplex pivot starting from the basic feasible solution x=(4,0,6,0). Show that the resulting basic feasible solution is optimal. (c) (10 points) Use the updated tableau to find a feasible solution x and a direction dR4 so that the set of optimal solutions can be written S={xR4:x=x+tdfort0}. (d) (5 points) Give an optimal solution with x2=2

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