Consider the following optimization problem Minimize 3x1+8x2 s.t. 2x1+6x2 > 6 x1+2x2 > 2.5 x1+3x2 > 0.5 x1>0 x2>0 a) Graph the feasible region of this linear program. Is the feasible region bounded? Why? (you may use an online tool like desmos.com/calculator) b) Are any of the above constraints redundant? If so, indicate which one(s). Explain why. c) Solve the linear program using the graphical method. Explain your approach. d) Consider the feasible region drawn in Part (a) and answer the following: If we add the constraint 3x1+x2> a (hint: you may use desmos.com/calculator and shift the parameter a to see how the feasible region changes) i. For what values of a is this a redundant constraint, if any? Why? ii. For what values of a is the above optimal solution no longer optimal, if any? Why? iii. For what values of a does the problem become infeasible, if any? Why? e) Consider the original formulation (without the added constraint). We will replace the original objective function 3 x1+8x2 with 3x1+b x2. For what values of b, will there be alternative optima (hint: recall that to get alternative optima the objective function line coincides with one of the constraints)