Optimization chooses the best feasible row, not just any feasible row. This is CP-SAT-style exhaustive search on tiny data; real solvers use propagation and clause learning.

Example

Optimization chooses the best feasible row, not just any feasible row. This is an exhaustive-search view on tiny data; unlike a real CP-SAT solver, it does not propagate constraints or learn clauses.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6\begin{array}{c|c}\text{x=0 y=3}&\hlmath{\text{value=3x+2y=6}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\hlmath{\text{value=3x+2y=5}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\hlmath{\text{value=3x+2y=7}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\hlmath{\text{value=3x+2y=9}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9x=2 y=0value=3x+2y=6\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\hlmath{\text{value=3x+2y=6}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9x=2 y=0value=3x+2y=6x=2 y=1value=3x+2y=8\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\hlmath{\text{value=3x+2y=8}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9x=2 y=0value=3x+2y=6x=2 y=1value=3x+2y=8x=2 y=2value=3x+2y=10\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\hlmath{\text{value=3x+2y=10}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9x=2 y=0value=3x+2y=6x=2 y=1value=3x+2y=8x=2 y=2value=3x+2y=10x=3 y=0value=3x+2y=9\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\text{value=3x+2y=10}\\\text{x=3 y=0}&\hlmath{\text{value=3x+2y=9}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9x=2 y=0value=3x+2y=6x=2 y=1value=3x+2y=8x=2 y=2value=3x+2y=10x=3 y=0value=3x+2y=9x=3 y=1value=3x+2y=11\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\text{value=3x+2y=10}\\\text{x=3 y=0}&\text{value=3x+2y=9}\\\text{x=3 y=1}&\hlmath{\text{value=3x+2y=11}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

x=0 y=3value=3x+2y=6x=1 y=1value=3x+2y=5x=1 y=2value=3x+2y=7x=1 y=3value=3x+2y=9x=2 y=0value=3x+2y=6x=2 y=1value=3x+2y=8x=2 y=2value=3x+2y=10x=3 y=0value=3x+2y=9x=3 y=1value=3x+2y=11verdictbest x=3 y=1 value=11\begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\text{value=3x+2y=10}\\\text{x=3 y=0}&\text{value=3x+2y=9}\\\text{x=3 y=1}&\text{value=3x+2y=11}\\\text{verdict}&\hlmath{\text{best x=3 y=1 value=11}}\end{array}
logic-computation Every row is intentionally ordered and pinned to the lesson specification.