Overview of Week 2
Math 407 Section A
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Reading Assignment:
- Course notes: Section 1:
Introduction, Due Wednesday, Oct 2.
- Course notes: Section 2: pages 1-6:
Due Monday, Oct 7.
- Course notes: Section 2: pages 6-12:
Due Friday, Oct 11.
- Course notes:Section 2: pages 12-16:
Due Monday, Oct 14.
- Course notes:Section 3: pages 31-37:
Due Wednesday, Oct 16.
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Homework Assignment:
-
Vocabulary List:
- Section 1 Notes:
- decision variable
- linear function
- linear inequality
- the solution set of a system of linear inequalities
- objective function
- linear programming
- explicit and implicit linear constraints
- the 4 steps in LP modeling
- standard form
- optimal value
- optimal solution
- feasible solution
- infeasible LP
- unbounded LP
- optimal value function
- sensitivity analysis
- the marginal value of a resource (shadow prices)
- the dual of an LP in standard form
- the Weak Duality Theorem
- Section 2:
- slack variables
- objective variable
- the initial dictionary (standard form)
- the initial tableau (standard form)
- dictionary (for an LP in standard form)
- simplex tableau (for an LP in standard form)
- feasible solution
- feasible dictionary
- basic solution
- basic feasible solution
- basic variables in a dictionary
- nonbasic variables in a dictionary
- a basis for a dictionary
- pivot row
- pivot column
- pivoting
- What is the rule for choosing the entering variable?
- What is the rule for choosing the leaving variable?
- optimal dictionary
- optimal tableau
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Key Concepts:
- Section 1:
- What is an LP?
- the 4 steps of LP modeling
- graphical solutions of two dimensional LPs
- sensitivity analysis
- standard form
- the Weak Duality Theorem
- Section 2:
- Dictionaries
- simplex tableau
- Basic feasible solutions
- The basis associated with a dictionary
- A simplex pivot and the simplex algorithm
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Skills to Master:
- solving 2 dimensional LPs graphically
- LP modeling
- transformation of an LP to standard form
- Setting up a dictionary
- Setting up a tableau
- Pivoting and the simplex algorithm for problems with
feasible origin.
Quiz:
Friday, Oct 4.
- This quiz is based on the vocabulary words and homework associated with
Section 1 of the online
notes. A selection from these vocabulary words throught "unbounded LP" will
comprise the first question on the quiz. In the second question
you will be asked to
solve a 2 dimensional LP graphically.
In this regard, you
must follow all of the steps described in class and in the notes.
Bring graphing aids (straight-edge and pencil) to the quiz!