To write:
The initial simplex tableau for the given problem and the pivot element to be used for the first iteration of the simplex method is to be identified.
Answer to Problem 1BMO
Solution:
Constant | |||||||
The pivot element is
Explanation of Solution
Given:
The given conditions are,
Approach:
(1) If all the entries are nonnegative, the optimal solution has been reached.
(2) If there is one or more negative entries, the optimal solution has not been reached.
Calculation:
Consider the given objective function.
Maximize
Introduce the slack variables,
The initial simplex table is as follows,
Constant | |||||||
Table
Calculate the pivot element.
All the element in the last row are not non negative. So, the above simplex table is not in its final form.
The most negative element in the last row is
So, the pivot column is column
Calculate the pivot row.
Constant | Ratio | |||||||
The least ratio is
Therefore, the element corresponding to pivot column and the pivot row is
Conclusion:
Hence, the initial simplex table is shown in Table
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