Building the simplex tableau
With every equation in the same format, you load the coefficients and the right-hand totals into a matrix, one row per equation. The objective function goes in the top row. At the start of the search nothing has been produced yet, so the revenue entry reflects that starting point.
One deliberate twist: multiply the entire top row by $-1$. This is a convention that lets the rest of the algorithm look for the largest negative number to decide where to go next, rather than the largest positive one. It changes nothing about the underlying problem, it just aligns the numbers with how the method is usually written.
The rest is bookkeeping. It helps to draw a dotted line separating the objective-function coefficients from the constraint coefficients, and another separating the left sides of the equations from the totals on the right. Labeling each column, one for cookie, one for donut, one per slack variable, and one for the totals, keeps track of what each number means. That labeled matrix is the tableau the simplex algorithm operates on.
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- Topic: Simplex algorithm, StatQuest
- Difficulty: Intermediate
- Completed: 0 users