Homework for Week 4
Math 408 Section A, January 26
-
Reading Assignment:
- Portfolio Modeling Using LPs : Due Friday, January 23.
- Linear Programming Primer : Due Monday, January 26.
- Multivariable Calculus Review: Due Wednesday, January 28.
- Optimality Conditions for Unconstrained Problems: Due Monday, February 2.
-
Homework Assignment:
- LP Primer:
- Be able to solve a 2 variable LP graphically.
- Be able to state and prove the Weak Duality Theorem for
LPs in standard form.
- Be able to transform any LP to one in standard form.
- Linear Programming Duality:
- Be able to state the Strong Duality Theorem for
LPs in standard form.
- LP Modeling:
- Be able to model the modeling problems
1, 2, 3, 4, and 5 as LPs.
- LP Duality:
- Be able to compute the dual of a general LP concretely specified,
i.e. with the coefficients given numerical values.
- Be able to compute the dual of a general LP abstractly specified,
i.e. in matrix notation.
-
Vocabulary List:
- Linear Programming Duality
- LP Standard Form
- Weak Duality Theorem
- Strong Duality Theorem
-
Key Concepts:
- LP duality, weak and strong duality theorems
- LP Standard Form
- LP Duality Theory.
- LP Modeling
-
Skills to Master:
- Transforming an LP into Standard Form.
- Solving 2 variable LPs graphically.
- Computing the dual to a general LP.
- Modeling LPs
-
Quiz:
-
The quiz will have two questions. The first question will be worth 30
points and will ask you to either (a) solve a two variable LP graphically,
(b) transform and LP into standard form, or (c) write the dual of an
arbitrary LP.
The second question is worth 20 points and will ask you to
model a problem as an LP.