Lofton Company has developed the following linear programming problem

Max x₁ + x₂

Subject to:

2x₁ + x₂ < 30 Constraint 1

3x₁ + 4x₂ < 60 Constraint 2

2x₁ + x₂ > 40 Constraint 3

Unfortunately, as a linear programming problem, it was infeasible. As a revision, Lofton dropped the original objective and established the following three goals:

Goal 1 (Priority 1): Don't exceed 30 in constraint 1

Goal 2 (Priority 1): Don't exceed 60 in constraint 2

Goal 3 (Priority 2): Don't fall below 40 in constraint 3

A. What are the goals for the problem (state as equations)? (9 pts)

B. What is the goal programming objective function for this goal programming problem? (3 pts)

C. Draw a graph showing all goals and economic constraints (if any) and identify the coordinates to consider as potential solutions. (18 pts)

D. Using the process covered in class, determine the optimal combination of X1 and X2 to satisfy your objective. (6 pts)

E. If an economic constraint of 2x1+2x2 <=80 was introduced into the scenario, would that change your answer? (You dont need to resolve to answer this.) Yes or no? Explain in one brief statement. NOTE: If you write more than one statement, you will receive ZERO points.