Mathematical Optimization for Business Problems Cognitive class Final Exam Answers:-

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Course Name :- Mathematical Optimization for Business Problems

Module 1 :- The Big Picture

Question 1 : True or false? Constraint Programming is particularly useful for solving scheduling problems and certain combinatorial optimization problems.

• False
• True

Question 2 : True or false? A feasible solution can be, but is not guaranteed to be, an optimal solution.

• False
• True

Question 3 : True or false? Objective functions always start with the words “maximize” or “minimize”.

• False
• True

Module 2:- Linear Programming

Question 1 : 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 2 : True or false? Hard constraints can be converted to soft constraints to help resolve infeasibilities.

• False
• True

Question 3: True or false? If a constraint is non-binding, its dual price will be zero.

• False
• True

Module 3 :- Network Models

Question1 : 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 2 : True or false? The critical path is the shortest path in the network.

• False
• True

Question 3 : True or false? A sequence of arcs connecting two nodes is called a path.

• False
• True

Module 4 :- Beyond Simple LP

Question 1 : True or false? A piecewise linear function can be used to approximate convex nonlinear functions.

• False
• True

Question 2 : True or false? The branch and bound method begins with LP relaxation.

• False
• True

Question 3 : True or false? Mixed-integer programming is often used for investment planning.

• False
• True

Module 5:- Modelling Practice

Question 1 : True or false? Data sparsity can be exploited to create only the essential variables and constraints, thus reducing memory requirements.

• False
• True

Question 2 : True or false? It is important to always use integer variables when a model involves the production of whole items.

• False
• True

Question 3 : True or false? It is important to use penalties only when absolutely necessary.

• False
• True

Mathematical Optimization for Business Problems Cognitive class  Final Exam Answers:-

Question 1 : What are the two types of objects used to describe network structures?

• Nodes and arcs
• Arcs and chains
• Nodes and chains

Question 2 : What are the possible reasons for an infeasible model?

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

Question 3 : True or false? Mathematical programming and constraint programming are the techniques you can apply using CPLEX.

• False
• True

Question 4 : True or false? Binary variables are also known as Boolean variables.

• False
• True

Question 5 : 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 6 : True or false? Basic variables take zero values in an iteration or final solution of the Simplex method.

• False
• True

Question 7 : True or false? An unbounded variable always influences the solvability of a model.

• False
• True

Question 8 : True or false? Flow conservation constraints are typically used in network models.

• False
• True

Question 9 : True or false? Nonlinear terms and absolute values are not permitted in linear programming.

• False
• True

Question 10 : True or false? Piecewise linear programming is used when dealing with functions consisting of several nonlinear segments.

• False
• True

Question 11 : True or false? Very large linear programming models are often non-sparse.

• False
• True

Question 11 : What does an optimization-based solution involve?

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

Question 12 : 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 13 : 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 14 True or false? The scale of numbers used in an LP problem can affect computational time.

• False
• True