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1: Linear Programming
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2: Profit Function
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3: Contour Lines
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4: Simplex Algorithm
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5: Simplex Algorithm for Solving LP Problems
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6: Tableau Review
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7: Simplex Tableau – Slack Variables
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8: Simplex Tableau – Slack Variables
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9: Simplex Tableau – Basic Variables and the Solution
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10: Tableau Solution
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11: Pivoting the Tableau – When to Stop
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12: Finding the Pivot Column
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13: Finding the Pivot Row
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14: Pivot Row Review
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15: The Pivot Operation
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16: Pivot Review
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17: Solving the Whole Simplex
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The "pivot" operation is what we execute on the tableau to simulate the movement from one vertex of the feasible region to the next. Pivoting continues while at least one of the coefficients in the bottom row is negative (excluding the last element, the "profit" variable).
If the objective function has a negative coefficient, it means the variable represented by that coefficient can be increased in order to increase the "profit" value. As such, we need to make that variable basic, swapping out its "basicness" for another variable by pivoting it.
Don't worry that we haven't gone over the actual pivoting yet. That will come soon.
Complete the should_pivot method. It should return True if any element in the self.objective list is negative, excluding the last element. Otherwise return False.