iz XI 2 3 x4 5 6 Right side 0 2 )|0 2 (2)0 20 Use the fundamental insight to identify the missing numbers in the final simplex tableau 6. Consider the following problem(20 points) Maximize Z=2x,+7x2-3x3 x1+3x2+4x3≤30 subject to{x1+4x2-x3≤10 x≥0,x2≥0,x3≥0 The corresponding final set of equations yielding the optimal solution is (0) x2+ +2x。=20 x2+5x3+x4-x6=20 (2) +4x2- Now you are to conduct sensitivity analysis by independently investigating each of the following changes in the original model. For each change, use the sensitivity analysis procedure to determine whether the previous optimal solution is till optimal (a)Change the right-hand sides to b2」[30 (b)Change the coefficients of x, to a,3= 3 2 (c)Introduce a new variable x6 with coefficients am=1 (d)Introduce a new constraint 3x,+2x,+3x2 <25 (e)Change constraint 2 to x,+2x2+2x, <35 7. A contractor has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below Hauling cost per ton at site Price per ton3 Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 2 0 2 X5 (1) 0 1 1 2 X3 (2) 0 -2 0 4 X1 (3) 0 1 0 -1 Use the fundamental insight to identify the missing numbers in the final simplex tableau. 6. Consider the following problem (20 points) ⎪ ⎩ ⎪ ⎨ ⎧ ≥ ≥ ≥ + − ≤ + + ≤ = + − 0, 0, 0 4 10 3 4 30 2 7 3 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 (2) 4 10 (1) 5 20 (0) 2 20 1 2 3 5 2 3 4 5 2 3 5 + − + = − + + − = + + + = x x x x x x x x Z x x x Now you are to conduct sensitivity analysis by independently investigating each of the following changes in the original model. For each change, use the sensitivity analysis procedure to determine whether the previous optimal solution is till optimal. (a) Change the right-hand sides to ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 30 20 2 1 b b (b) Change the coefficients of x3 to ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 3 2 23 13 3 a a c (c) Introduce a new variable x6 with coefficients ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡− = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 1 3 21 11 6 a a c (d) Introduce a new constraint 3x1 + 2x2 + 3x3 ≤ 25 (e) Change constraint 2 to x1 + 2x2 + 2x3 ≤ 35 7. A contractor has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1,2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Hauling cost per ton at site Pit 1 2 3 Price per ton