# Simplex Algorithm Problem

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6. Consider the problem

maximise 2x_1 + 3x_2 + x_3

subject to x_1 + 2x_2 + 3x_3 + x_4 = 6

2x_1 + x_2 + 2x_3 + x+5 = 4

x_1, ..., x_5 >= 0

with initial tableau:

1 2 3 1 0 | 6

2 1 2 0 1 | 4

-------------

2 3 1 0 0 | 0

and final tableau:

. . . 2/3 -(1/3) | .

. . . -(1/3) 2/3 | .

---------------------

. . . -(4/3) -(1/3) | .

Without going through the simplex algorithm, fill in the other numbers in the final tableau. Suppose that you now wish to change the problem by adding a term +2x_6 to the objective function and a term +x_6 to the left-hand side of the first constraint. Show how to add an extra column to the final tableau (again without using the simplex algorithm) to accommodate this change. Complete the solution of the new problem using the simplex algorithm.

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##### Solution Summary

In a detailed, hand written response provided in JPG format, this answer finds the solution to the final tableau numbers.

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