**Typically offered during the spring semester.**

Use of deterministic models and computers to study and optimize systems. Includes an introduction to modeling, calculus-based models, financial models, spreadsheet models, and linear programming models.

MTH 251

- Introduction to models and how models are used (1.5)
- introduction to mathematical models, advantages, disadvantages
- classification of mathematical models
- mathematical model terminology
- examples of mathematical needs
- model formulation

- Model examples (3)
- calculus based optimization models
- financial models
- spreadsheet models
- non linear models
- solving simple unconstrained problems by search

- Introduction to linear programming, problem formulation (2)
- Systems of equations and matrix algebra (.5)
- Simplex algorithm (2)
- Sensitivity analysis and duality (2)
- Heuristic search methods (1)
- Optional optimization applications (2)
- Transportation problem
- Assignment problem
- Network models
- Data envelopment analysis
- Other applications

- Exams/Review (1)

- To be able to use calculus to formulate and solve non linear optimization problems.
- The student can formulate and solve multiple variable, unconstrained optimization problems.

- To be able to use linear programming to formulate and solve linear optimization problems.
- The student can formulate standard linear programming problems such as diet, scheduling, budgeting, and blending problems.
- The student can solve two variable linear programming problems graphically and explain the concepts feasible solution, infeasible solution, optimal solution, active constraint, inactive constraint, multiple optimal solutions, unbounded solutions, and no feasible solutions.
- The student can solve multiple variable linear programming problems using the simplex method and explain the concepts basic solution, basic feasible solution, adjacent basic feasible solution, basic variable, non basic variable, corner point, slack variable, surplus variable, artificial variable, reduced cost, shadow price, and degenerate basic solution.
- The student can solve linear programming problems using a software tool.
- The student can represent a linear programming problem and its solution in matrix form.
- The student can perform sensitivity analysis to interpret the impact of changes in the objective coefficients, the constraint coefficients, and the constraint limits.
- The student can formulate and solve one or more special types of linear programming problems such as goal programming problems, transportation problems, network problems, data envelopment problems, integer programming problems, or others.

- To enhance the student's ability to use quantitative models in decision making.
- The student can create optimization models for a wide variety of application areas.
- The student can explain the role of models in problem solving.
- The student can explain the role of data in modeling and is able to perform simple data analysis tasks.
- The student is able to formulate a decision problem in terms of controllable variables, constraints, and objectives.
- The student is able to construct simple financial models to compare investment alternatives considering time value of money and taxes.

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