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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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This lesson's interactive features are locked, please to keep using them
As we've seen, a linear program can be represented in a tableau, which is just a fancy word for a matrix.
The tableau is useful because it allows us to keep track of the state of the program (moving around the vertices of the graph) without storing all the vertices explicitly.
To answer the questions, use this data from our bakery example, where cakes = x and cookies = y.
profit = (x * 5) + y
or
profit - 5x - y = 0
x <= 250
y <= 200
x + y <= 300
0 <= x
0 <= y
self.constraints = [250, 200, 300]
# Tableau
self.rows = [
[1.0, 0.0],
[0.0, 1.0],
[1.0, 1.0],
]
self.objective = [-5.0, -1.0]