4. Problem (40 points total) Consider the primal dual relationship. The following figure together with Primal-Dual Table at the top of exam may be helpful to recall the notation. Primal problem Dual problem "I i Zc-x-=Z W=21biyi i=1 a) (15 pts) Discuss relationship between feasible solutions primal and dual problem solutions, relationship between optimal solutions, what does the fact that Z is unbounded (for the primal problem) imply about the dual? b) (10 pts) Construct the dual problem for the following modification of Wyndor Glass problem. Maximize Z :3 x1 + 5X2 +K xneW, subject to xl + xnews 4 2x2 +xnew S 12 3x1 + 2X2 + Knew S 18; And all the usual non-negativity constraints. m that we added the third product, expressed by decision variable xnew, with profit value being K thousands of dollars per batch of this new product. Start by writing new matrixA corresponding to this modied problem. (c) (15 pts) Recall that for the original Wyndor problem we had Row 0 Table 6.5 for every iteration given at the top of the exam paper. Use this information to determine the maximum value for parameter K where the optimal solution does not include producing any amount of new product. In other words, find the maximum value for K where Xnew = 0 in the optimal solution. : You only need to utilize Table 6.5 information corresponding to the optimal solution