Exam Practice

Exam practice is organized around the recurring written-exam tasks.

See

• Solved Exam Template

  • the exact workflow to imitate.

• Formulation Drill Set

  • modeling from word problems.

• Graphical Drill Set

  • two-variable graphical solutions.

• Standard Form Drill Set

  • conversions into $Ax=b$, $x\ge0$.

• BFS and Reduced Cost Drill Set

  • BFS verification and optimality checks.

• Two Simplex Iterations Drill Set

  • revised and tableau simplex practice.

• Mixed Exam Problems

  • full exam-style combinations.

Fast classification

When reading an exam question, first classify it:

1. formulation only;
2. graphical solution;
3. standard form;
4. BFS verification;
5. reduced cost and optimality;
6. simplex iterations;
7. solver computation.

What to always show

• decision variables and units;
• objective function;
• all constraints;
• sign restrictions;
• standard-form variables if needed;
• candidate solution vector;
• basis matrix if checking BFS;
• reduced costs if checking optimality;
• objective value in the original objective;
• final sentence interpreting the result.

Common traps

• assuming $x_1,x_2\ge0$ when the problem does not say it;
• adding a slack variable to a $\ge$ constraint instead of a surplus variable;
• forgetting to multiply a negative RHS row by $-1$ when needed;
• checking BFS before lifting the point into standard form;
• mixing maximization and minimization reduced-cost signs;
• forgetting that basic variables have reduced cost zero;
• giving a point without the objective value.

See Also

• [[ Course Coherence Audit ]]
• [[ Exam Coverage Matrix ]]

Exam checkpoint

Practice under exam timing. Write the full pipeline: model, standard form if needed, BFS/reduced costs if asked, simplex iterations if asked, final objective value and interpretation.