Consider the following linear programming problem and its optimal final solution: max 2x1 + x2 - x3 s.t. x1 + 2x2 + x3 8 -x1 + x2 - 2x3 4 x1, x2, x3 0

The optimal solution is x1 = 8, x2 = 0

a. If you were to choose between increasing the right-hand-side of the first and second constraints, which one would you choose? What is the effect of this increasing on the optimal value of the objective function?

b. Suppose that a new activity x6 is proposed with unit return 4 and consumption vector a6 = (1,2).Find the new optimal solution

Please provide detailed process for each solution