Consider the following linear programming formulation:

min x + 4y

s.t 2y + x \geq 4

4y - x \geq -1

x \leq 5

x \geq 0

y \geq 0

(a) Graph all constraints and clearly identify the feasible region for the solution. Make sure to clearly label which line on the graph corresponds to each constraint.

(b) Solve the LP using the graphical method (also called the iso-profit line method) and the corner (extreme) point method and state the optimal solution and the optimal objective function value.

(c) Which constraints are binding in the optimal solution?

(d) Consider removing the y ? 0 constraint from the problem. Does doing this change the feasible region? Explain why or why not.

(e) Consider adding the constraint ‘x, y are integer’ to the original problem, explain how the feasible region changes.

Please show all work for all parts.