Purchase Solution

Use the Karush-Kuhn- tucker conditions to solve

Not what you're looking for?

Ask Custom Question

1. Consider the LP Max z=c1x1+2x2+c3x3
Subject to x1 + 5x2+a1x3 ≤ b1
X1-5x2+a2x3≤ b2
X1, x2, x3 ≥ 0
The optimal tableau for this LP is

1 d1 2 1 0 30
0 d2 -8 -1 1 10
0 d3 -7 d4 0 z - 150

Without using the simplex method, determine all unknown constants in this problem
(i.e., a1,a2,b1,b2, c1, c3, d1,d2, d3, d4)

2. Consider the following problem:
Maximize z= 6x1 + 8x2
Subject to 5x1 + 2x2 less than or equal to 20
x1 + 2x2 less than or equal to 12
x1, x2 greater than or equal to 0
(a) Sketch the feasible set and solve the program geometrically
(b) Determine all the basic solutions for this program and indicate them on the sketch in (a). Which ones are feasible? (there are 6 basic solutions, not all feasible).
(c) Solve the program by the simplex method. For each tableau, indicate which feasible solution corresponds to it
(d) Write the dual of this program. For each primal basic solution, determine the corresponding dual basic solution that satisfies the complementary slackness principle. Which ones are dual feasible?

3. Consider the system of equations -x1+x2-x3=3, -x1+2x2-x4=2, and x1+x2+x5=2
(a) by converting the equations into inequalities in two variables, show geometrically that there are no nonnegative solutions to this system.
(b) use the simplex method to show the same thing

4. Use the Karush-Kuhn conditions to solve:
Maximize z=2x1+x2+3x3
Subject to x1+2x2+x3 less than or equal to 12
X1,x2,x3 greater than or equal to 0

Purchase this Solution

Solution Summary

This solution provides step by step calculations for questions using the Karush-Kuhn condition.

Purchase this Solution

Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability