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

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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

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

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