Maximize z=x-x+2 2x1-2x2+3x3≤5 ≤3 subject to +x,≤2 ≥0.x2≥0.x,≥0 Let x4, x5, and x6 denote the slack variables for the respective constraints. After you apply the simplex method, a portion of the final simplex tableau is as follows Basic variable Z XI X2 X3 X4 X5 6 Right side (0) X6 (2)0 0 (3)0 Use the fundamental insight to identify the missing numbers in the final simplex tableau 6. Consider the following problem(20 points) Maximize Z=3x,+x+4x 6x+3x,+5x2≤25 subject to 3x,+4x+5x.<20 ≥0,x2≥0,x3≥0 The corresponding final set of equations yielding the optimal solution is +-x,+-x。=17 (1) x5 x2+x35 x,+=X。=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 from the final set of equations (d)If coefficient of x2 is changed to a2=2 Determine whether the previous ptimal solution is till optimal (e)If a new variable Xnew has been introduced into the model, Xnew coefficient is3 ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≥ ≥ ≥ − + ≤ + − ≤ − + ≤ = − + 0, 0, 0 2 3 2 2 3 5 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x x x x subject to Maximize Z x x x Let x4,x5, and x6 denote the slack variables for the respective constraints. After you apply the simplex method, a portion of the final simplex tableau is as follows: Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 1 1 0 X2 (1) 0 1 3 0 X6 (2) 0 0 1 1 X3 (3) 0 1 2 0 Use the fundamental insight to identify the missing numbers in the final simplex tableau. 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