Purchase Solution

Linear Programming : Scaling, Unbounded LPs and Feasible Region

Not what you're looking for?

Ask Custom Question

Question #1
A company produces three products. The per-unit profit, labor usage, and pollution produced per unit are given in the table 1. At most, 3 million labor hours can be used to produce the three products, and government regulations require that the company produce at most 2 lb of pollution. If we let Xi = units produced of product i then the appropriate LP is
Max
s.t.

a. Explain why this LP is poorly scaled.
b. Eliminate the scaling problem by redefining the units of the objective function, decision variables, and the right hand sides.
Table 1
Product Profit($) Labor Usage(Hrs) Pollution (Lb)
1 6 4 0.000003 lb
2 4 3 0.000002 lb
3 3 2 0.000001 lb

Question #2
Show that the following LP is unbounded:
Max
s.t.

Find the point in the feasible region with

Question #3
Suppose that in solving an LP, we obtain the tableau in Table 2. Although x1 can enter the basis, this LP is unbounded, Why?
Z X1 X2 X3 X4 rhs
1 -3 -2 0 0 0
0 1 -1 1 0 3
0 2 0 0 1 4
---

Attachments
Purchase this Solution

Solution Summary

Linear Programming, Scaling, Unbounded LPs and Feasible Region are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

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

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.

Graphs and Functions

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