Overview
Review Questions for Mid-term
For Part I of the mid-term exam, there will be 4-5 questions from the list below.
1. What are the differences between stochastic and deterministic models? What are the
differences between prescriptive and descriptive models?
2. List three areas/fields where linear programming and related optimization techniques are
commonly used. Give an example for each.
3. Name 3 common rules for modeling.
4. What are the 4 components of a mathematical program? What makes it a linear program?
5. What are the different types of possible solutions to a linear program?
6. Briefly explain the intuition behind the graphical approach of solving simple LPs.
7. Briefly explain the essence of the simplex method (i.e. how does it work?).
8. Briefly explain the meaning of a dual/shadow price. How can you obtain the dual prices
by formulating the dual problem?
9. How do you go back to the standard/canonical form for a LP when:
a. You have an inequality constraint?
b. You want to change the objective to maximize from minimize?
c. A variable is not constrained?
10. How do we know with in the simplex (tableau or basis representation) that the current
solution is optimal?
11. How do you know in the simplex (tableau or basis representation) that there is more than
one optimal solution?
12. What is the strong duality theorem for linear programs?
Part II of the mid-term exam will have 2 to 3 longer problems. Key skills for longer
problems:
I. Given a problem statement, know how to formulate the corresponding mathematical
program.
II. Given a linear program, know how to write it in standard form and how to formulate
its dual linear program.
III. Know how to perform full steps of the simplex.
IV. Know how to interpret the final tableau or final basis representation of the simplex to
extract the full solution, and to verify that the solution is optimal.
V. Know how to interpret the Excel Solver sensitivity report.
VI. Know how to graphically solve a simple linear program with 2 decision