Original Problem: Consider the following problem with the following initial and final tableaux. XI x2 x3...

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Original Problem: Consider the following problem with the following initial and final tableaux. XI x2 x3 X4 x5 x6 x5 3 1 2 4 x6 8 2 -1 7 0 0 91 28 1 50 Maximizing z=11x1 +4x2+x3+15x4 -11 -4 -1 -15 0 0 0 subject to 3x1 + x2 + 2x3 + 4x4 <28 x4 -2 0 5 1 2 -1 9 8x12x2- - x3+7x450 X2 11 1 -18 0 -7 4 4 3 X1, X2, X3, X4 0 0 2 0 2 1 106 Section 5.4: Suppose a variable x, is added to the Original Problem such that the problem becomes: Max 11 x + 4x2 + x3 + 15 + 3 + x 2 + 2 x3 + 4 4 + x, 28 8x + 2x2 - x3 + 7x4 + Yx7 50 x 1 X1, X2, X3, X4, X, 0 2' '3' '4' Solve the problem for each of the following cases using the given original tableaux (without x7) above. 1. = 9, B = 2, y = 5 2. = 27, = 7, y = 12 Section 5.6 Suppose changes were made to the Original Problem (without x-) such that 50 in the RHS of the second constraint is changed to 50+. * * 1. What is the new expression of b and Z 2. Starting from the given tableaux above and with any additional tableaux if needed, solve for the optimal value and point if == 2. Section 5.7 Going back to the Original Problem (without x, and with 50 in the RHS), for each case (separately) below, solve the problem after adding the given constraint: 1. 3 + x2 + 3x 24 1 2. 3x1 4 + + 3x 20 +2 4 Original Problem: Consider the following problem with the following initial and final tableaux. XI x2 x3 X4 x5 x6 x5 3 1 2 4 x6 8 2 -1 7 0 0 91 28 1 50 Maximizing z=11x1 +4x2+x3+15x4 -11 -4 -1 -15 0 0 0 subject to 3x1 + x2 + 2x3 + 4x4 <28 x4 -2 0 5 1 2 -1 9 8x12x2- - x3+7x450 X2 11 1 -18 0 -7 4 4 3 X1, X2, X3, X4 0 0 2 0 2 1 106 Section 5.4: Suppose a variable x, is added to the Original Problem such that the problem becomes: Max 11 x + 4x2 + x3 + 15 + 3 + x 2 + 2 x3 + 4 4 + x, 28 8x + 2x2 - x3 + 7x4 + Yx7 50 x 1 X1, X2, X3, X4, X, 0 2' '3' '4' Solve the problem for each of the following cases using the given original tableaux (without x7) above. 1. = 9, B = 2, y = 5 2. = 27, = 7, y = 12 Section 5.6 Suppose changes were made to the Original Problem (without x-) such that 50 in the RHS of the second constraint is changed to 50+. * * 1. What is the new expression of b and Z 2. Starting from the given tableaux above and with any additional tableaux if needed, solve for the optimal value and point if == 2. Section 5.7 Going back to the Original Problem (without x, and with 50 in the RHS), for each case (separately) below, solve the problem after adding the given constraint: 1. 3 + x2 + 3x 24 1 2. 3x1 4 + + 3x 20 +2 4