Iterating to the optimum, and a three-variable run
After one pivot you repeat the same three steps: scan the top row for the largest negative entry to pick the next entering column, run the ratio test to see how far to move, then reduce that column to read off the new vertex coordinates and revenue in the upper-right corner.
When do you stop? Scan the top row once more: if there are no negative numbers left, no direction can raise revenue, so you are done.
The same machine handles the fancier three-product problem. Rename donut, cookie, and brownie as $x$, $y$, and $z$ to keep the algebra readable. With five constraints you add five slack variables, one per constraint, build the matrix, and negate the top row. Then you pivot repeatedly until the top row has no negatives left, at which point the tableau gives the optimal mix amounts and revenue.
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- Topic: Simplex algorithm, StatQuest
- Difficulty: Intermediate
- Completed: 0 users