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# Linear Programming by the Simplex Method and Input-Output Matrices ( Input/Output Matrix ) (13 Problems)

Please see the attached file for the fully formatted problems.

#### Solution Preview

Please see the attached file for the complete solution.

As we can introduce new variables to write the inequalities to equalities as follows.

So, (A) could be correct if we changed the 4th 5th and 6th columns to be

-1 0 0
0 -1 0
0 0 -1
0 0 0

Question (2) (D)

The original LP and dual LP will have the equal optimal value 898.40. However, the solution corresponds to the coefficients in the dual objective function in the final tableau. Namely, x1=3.5, x2=4.0 and x3=2.4 in the 4th row.

Question (3) (B)

As we can introduce new variables to write the inequalities to equalities as follows.

Then we can see that only (B) has the first three rows match to the coefficients of the above equalities.

Question (4) (D)

Question (5) (A)

I attached the following tableaus.

Tableau #1
x y s1 s2 z
2 1 1 0 0 24
1 3 0 1 0 37
-10 -10 0 0 1 0

Tableau #2
x y s1 s2 z ...

#### Solution Summary

Thirteen problems relating to Linear Programming by the Simplex Method and Input-Output Matrices are investigated. The solution is detailed and well presented.

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