11. (18 pts) Consider the following problem: Maximize Z = x1 + 2x2 subject to x1 + 3x2 8 2x1 + x2 6 and x 0, x2 0. The optimal solution is (x1, x2) = (2,2), Z* = 6. Use the following three different approaches to find the shadow prices. (a) (10 pts) Use graphical analysis to find the shadow prices for the resources. (b) (2 pts) Use the last simplex tableau (given below) to find the shadow prices for the resources. BV Eq N x1 x2 x3 x4 RHS Z EqO 1 0 0 0.6 0.2 6 x2 Eq1 0 0 1 0.4 -0.2 2 x4 Eq2 0 1 0 -0.2 0.6 2 (c) (6 pts) Use the Excel Solver to solve the problem to find the optimal Z value, then modified each resource's RHS by adding 1 (do the modification to one functional constraint at a time), use the new optimal Z value and the old optimal Z value to find the shadow price.