4 - 6 - 2 3

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What is the corresponding system of equations? Restate the problem in terms of equations by adding slack variables or subtracting surplus variables as necessary. Then write the initial simplex tableau. X1 + X2 + X3 S1 = 69 Маximize Z-2x1 + 3x2 — 4xз X1 + X2 + X3 S2 = 48 X1 + X2 X1 20, x2 2 0, X3 0, s, 20, s2 2 0, s3 20 subject to X1 +X2 + X3 <69 + S3 = 60 X1 +X2 + X3 248 X1 +X2 < 60 Write the initial simplex tableau, omitting the z column. Fill in the missing values. X1 20, x2 2 0, X3 20 X1 X2 X3 S1 S2 $3 1 1 1 O 69 1 1 1 0 48 1 1 0| 60 4

Suppose the coefficient matrix associated with a linear system has a pivot in each row. Can we say, with certainty, that the linear system is consistent or inconsistent? Defend your response.