Homework 2 Solution
Exercise 1, page 89: Consider the following LP maximize subject to z = 2x1 + 3x2 x1 + 3x2 6 3x1 + 2x2 6 x1 , x2 0.
(a) Express the problem as a standard LP. (b) Determine all the b
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Lecture 14: Linear Programming Duality
September 27, 2010
The Dual Linear Program
Given an LP in the standard form,
max(min) z = s.t. c1 x1 a11 x1 a21 x1 . . . am1 x1 + + + c2 x2 a12 x2 a22 x2 . . . +
Lecture 13: Sensitivity analysis of Linear programs
September 22-24, 2010
Sensitivity Analysis
Study the impact of the changes in input data to the optimal value (solution). In general, there are thr
Lecture 9: Special Cases in Linear Programming
September 15, 2010
Four special cases
Degeneracy Multiple solutions Unbounded solution Infeasibility
Degeneracy
A tie for the minimum ratio test can hap
Lecture 7: Simplex Method III
September 10, 2010
Moving From One BFS to Another
Two adjacent vertices correspond to two BFSs whose basis have m 1 common basic variables (only one dierent basic variab
Lecture 6: Simplex Method II
September 8, 2010
Announcements
HW 1 is due on Friday 5 PM. Drop the HWs in the mailbox of the TA assigned to you. Get it time-stamped by someone in the office. Graded HW
Lecture 5: Simplex Method I
September 3, 2010
Announcements
GE 330 students must be registered concurrently in GE 397 for one credit hour. Homework 1 will be uploaded after class today Due on next Fri
Loan Policy Model
Thriftem Bank is in the process of devising a loan policy that involves a maximum of $12 million. The following table provides the pertinent data about available types of loans. Type
Lecture 4: Graphical Solution
August 30, 2010
Announcements
Labs begin this week Attendance will be taken in labs First homework will given on Friday Next lecture will be a problem solving lecture
Red
Lecture 3: Handling Nonlinearity
August 27, 2010
Nonlinear Programs
Is this a linear program?
Converting nonlinear programs to linear programs
This is an example of a nonlinear program.
A mathematical
Operations Research, GE330 - IE 310 Homework 1 Solutions
Exercise 1: (a) maximize subject to x1 x2 x1 + x2 = 2
It is not a linear program, since the objective function is not a linear function. (b) ma