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Mathematical Programming is a powerful technique used to model and solve optimization problems. This training provides the necessary fundamentals of mathematical programming and useful tips for good modeling practice in order to construct simple optimization models.

**Module 1 – The Big Picture**

**Question: True or false? Constraint Programming is particularly useful for solving scheduling problems and certain combinatorial optimization problems.**

**False**- True

**Question: True or false? A feasible solution can be, but is not guaranteed to be, an optimal solution.**

- False
**True**

**Question: True or false? Objective functions always start with the words “maximize” or “minimize”.**

- False
**True**

**Module 2 – Linear Programming**

**Question: True or false? The following constraint is valid for a linear programming problem, where x and y are variables and z is a data item: 2x + 3y less than or equal to z²**

- False
**True**

**Question: True or false? Hard constraints can be converted to soft constraints to help resolve infeasibilities.**

- False
**True**

**Question: True or false? If a constraint is non-binding, its dual price will be zero.**

- False
**True**

**Module 3 – Network Models**

**Question: True or false? In a transportation problem, if all the capacities and demands are integer, then you can declare the variables to be continuous even though they are integer.**

- False
**True**

**Question: True or false? The critical path is the shortest path in the network.**

**False**- True

**Question: True or false? A sequence of arcs connecting two nodes is called a path.**

**False**- True

**Module 4 – Beyond Simple LP**

**Question: True or false? A piecewise linear function can be used to approximate convex nonlinear functions.**

- False
**True**

**Question: True or false? The branch and bound method begins with LP relaxation.**

- False
**True**

**Question: True or false? Mixed-integer programming is often used for investment planning.**

- False
**True**

**Module 5 – Modelling Practice**

**Question: True or false? Data sparsity can be exploited to create only the essential variables and constraints, thus reducing memory requirements.**

- False
**True**

**Question: True or false? It is important to always use integer variables when a model involves the production of whole items.**

**False**- True

**Question: True or false? It is important to use penalties only when absolutely necessary.**

- False
**True**

**Final Exam**

**Question: What are the two types of objects used to describe network structures?**

**Nodes and arcs**- Arcs and chains
- Nodes and chains

**Question: What are the possible reasons for an infeasible model?**

- Real-world conflict
- Incorrect data
- Incorrect formulation
**All of the above**

**Question: True or false? Mathematical programming and constraint programming are the techniques you can apply using CPLEX.**

- False
**True**

**Question: True or false? Binary variables are also known as Boolean variables.**

- False
**True**

**Question: What is the first step of a typical optimization model development cycle?**

- The identification of objectives, variables, and constraints
**The scope definition**- The creation of a prototype

**Question: True or false? Basic variables take zero values in an iteration or final solution of the Simplex method.**

**False**- True

**Question: True or false? An unbounded variable always influences the solvability of a model.**

**False**- True

**Question: True or false? Flow conservation constraints are typically used in network models.**

- False
**True**

**Question: True or false? Nonlinear terms and absolute values are not permitted in linear programming.**

- False
**True**

**Question: True or false? Piecewise linear programming is used when dealing with functions consisting of several nonlinear segments.**

**False**- True

**Question: True or false? Very large linear programming models are often non-sparse.**

**False**- True

**Question: What does an optimization-based solution involve?**

- An optimization engine
- Data
- An optimization model
- All of the above

**Question: True or false? When all arcs in a chain are directed in such a way that it is possible to traverse the chain following the directions of arcs, it is called a path.**

- False
**True**

**Question: A region is convex if …**

- A straight line connecting two points inside the region passes outside it to get from one point to the other
**Any straight line between two points inside the region remains entirely in the region**- All of the above

**Question: True or false? The scale of numbers used in an LP problem can affect computational time.**

- False
**True**

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