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Math 484

Final Project

Spring 2022

1. Use the tableau implementation of the simplex algorithm to solve the following linear opti- mization problem:

− 6 1 + 5 2 − 8 3 + 3 4 ≥ −11

2 1 − 4 2 + 5 3 + 0 4 ≥ 7

 2 ≥ 0

Explain briefly all steps of your work.

You must show all tableaux. For each tableau, state explicitly

• the current basic variables;

• the current basic feasible solution and its objective value;

• the pivot column, the pivot row, and the pivot element;

• and the sequence of elementary row operations of the pivot to be performed on the current tableau.

The rows and columns of your tableaux must be labeled with the corresponding variables.

Warning: There are different conventions in use for tableaux. In order to receive credit, your tableaux must conform to the conventions ofBertsimas & Tsitsiklis. Tableaux set up according to other conventions will be ignored even ifyourfinal answer is correct.