1) Consider the following problem. MaxZ=3x1+x2+4x3subjectto6x1+3x2+5x3253x1+4x2+5x320x10,x20,x30 The corresponding final set of equations yielding the optimal solution is (0) Z+2x2+51x4+53x5=17 x131x2+31x431x5=35x2+x351x4+52x5=3 a. Identify the optimal solution from this set of equations. b. Construct the dual problem. c. Identify the optimal solution for the dual problem form the final set of equations. Verify this solution by solving the dual problem graphically. d. Suppose that the original problem is changed to: MaxZ=3x1+3x2+4x3subjectto6x1+3x2+5x3253x1+4x2+5x320x10,x20,x30 Use duality theory to determine whether the previous optimal solution is still optimal. e. Use the fundamental insight presented in Sec. 5.3. to identify the new coefficients of x2 in the final set of equations after it has been adjusted for the changes in the original problem given in part (d). f. Now suppose that the only change in the original problem is that a variable xnew has been introduced into the model as follows: MaxZ=3x1+x2+4x3+2xnewsubjectto6x1+3x2+5x3+3xnew253x1+4x2+5x3+2xnew20x10,x20,x30,xnew0 Use duality theory to determine whether the previous optimal solution, along with xnew=0, is still optimal. g. Use the fundamental insight presented in Section 5.3, to identify the coefficient of xnew as a non-basic variable in the final set of equations resulting from the introduction of xnew into the original model as shown in part (f)