Basic variable Coefficient of X1 X2 X3 X4 X5 Right side 03/21/2 X3 0 01/21/2 0-1/21/2 Use the fundamental insight to identify the missing numbers in the final simplex table Solution the final tableau is Basic variable E nt of XI 2 X3 4 X5 X6Right side 3/2 1)0 6. Consider the following problem(20 points) Maximize z=3x, +x+4 6x,+3x+5X,≤25 subject to 33x, +4x, +5x,<20 x1≥0,x2≥0,x3≥0 The corresponding final set of equations yielding the optimal solution is +-x,+-X=17 x +-x 35 x2 (a)Identify the optimal solution from this set of equations (b) Construct the dual problem (c)Identify the optimal solution for the dual problem from the final set of equations (d)If coefficient of x2 is changed to a,2=2. Determine whether the previous optimal solution is till optimal (e) If a new variable Xnew has been introduced into the model, Xnew coefficient is C6 3. Determine whether the previous optimal solution is till optimal Solution the final tableau is4 Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 0 3/2 1/2 X4 (1) 0 1 -1 -2 X3 (2) 0 0 1/2 1/2 X2 (3) 0 0 -1/2 1/2 Use the fundamental insight to identify the missing numbers in the final simplex tableau. Solution: the final tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 3/2 0 0 5 X2 (1) 0 1 0 0 5 X6 (2) 0 1/2 0 1 3 X3 (3) 0 -3/2 1 0 1 6. Consider the following problem (20 points) ⎪ ⎩ ⎪ ⎨ ⎧ ≥ ≥ ≥ + + ≤ + + ≤ = + + 0, 0, 0 3 4 5 20 6 3 5 25 3 4 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x subject to Maximize Z x x x The corresponding final set of equations yielding the optimal solution is 3 5 2 5 1 (2) 3 5 3 1 3 1 3 1 (1) 17 5 3 5 1 (0) 2 2 3 4 5 1 2 4 5 2 4 5 + − + = − + − = + + + = x x x x x x x x Z x x x (a) Identify the optimal solution from this set of equations. (b) Construct the dual problem (c) Identify the optimal solution for the dual problem from the final set of equations. (d) If coefficient of x2 is changed to ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 3 2 3 22 12 2 a a c . Determine whether the previous optimal solution is till optimal. (e) If a new variable Xnew has been introduced into the model, Xnew coefficient is ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 3 2 26 16 6 a a c . Determine whether the previous optimal solution is till optimal. Solution: the final tableau is