**Step 1** We convert the LP problem into a system of linear equations by putting in the slack variables and rewriting the objective function:

x | + | y | + | z | + | s | = | 40 | ||||||

2z | + | y | - | z | - | t | = | 10 | ||||||

- | y | + | z | - | u | = | 10 | |||||||

2x | 3y | z | + | p | = | 0 |

Thus, the initial tableau is as follows.

x | y | z | s | t | u | p | Ans |
||

s |
1 | 1 | 1 | 1 | 0 | 0 | 0 | 40 | |

t |
2 | 1 | -1 | 0 | -1 | 0 | 0 | 10 | |

u |
0 | -1 | 1 | 0 | 0 | -1 | 0 | 10 | |

p |
-2 | -3 | -1 | 0 | 0 | 0 | 1 | 0 |

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