Q1. Consider the following linear programming problem and its optimal final tableau shown below. max2x1+x2x3 s.t. x1+2x2+x38 x1+x22x34 x1,x2,x30 a. Write the dual problem and find the optimal dual variables from the above tableau. b.Using sensitivity analysis, find the new optimal solution if the coefficient of x2 in the objective function is changed from 1 to 5. c. For what range of b1 (the first constraint resource) will it remain feasible? d.Suppose that a new activity x4 is proposed with unit return 4 and consumption vector a4=(12). Find the new optimal solution