### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Math 125 Study Guide 35661

UIC

### View Full Document

## About this Document

## 30

## 0

## Popular in Elementary Linear Algebra

## Popular in Mathematics (M)

This 4 page Study Guide was uploaded by Lael Wynne on Friday April 1, 2016. The Study Guide belongs to 35661 at University of Illinois at Chicago taught by Roy Lowman in Spring 2016. Since its upload, it has received 30 views. For similar materials see Elementary Linear Algebra in Mathematics (M) at University of Illinois at Chicago.

## Reviews for Math 125 Study Guide

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 04/01/16

Math 125 Exam 2 Subjects covered on the exam (Sections 3.2-5.3): Transition matrix o Stable distribution probability Solving Linear Programming o Use of the simplex method (Maximize & Minimize) o Graphing Simplex Tableau o Pivoting o Slack variables o Objective value (min & max) o Sensitivity analysis Linear programming o Duality o Pivoting Trends o Percentage Absorbing Stochastic Matrix o The corresponding column as a single 1 and the remaining entries are 0 o The single 1 must be located on the main diagonal of the matrix Example 1: Absorbing matrix : 1 0 .3 0 I S 0 1 . 1 1 0 0 .5 0 0 R 0 0 .1 0 1) Identify S & R: S= .3 0 R= .5 0 .1 1 .1 0 2) Identify (I-R): 1 0 _ .5 0 = .5 0 0 1 .1 0 -.1 1 3) (I-R) (Can use calculator, matrix setting) .5 0 ^-1 = 2 0 -.1 0 .2 1 Example 2: A furniture manufacturer makes two types of furniture: chairs and sofas. The manufacture of a chair requires: 6 hours of carpentry, 1 hour of finishing, 2 hours of upholstery. Manufacture of a sofa requires: 3 hours of carpentry, 1 hour of finishing, 6 hours of upholstery. Each day the factory has available: 96 labor hours for carpentry, 18 labor-hours for finishing, 72 labor-hours for upholstery. The profit per chair is $80 and per sofa is $70. How many chairs and sofas should be produced each day to maximize the profit? Let x = number of chairs and y = number of sofas. X Y Resource Carpentry 6 3 96 Finishing 1 1 18 Upholstery 2 6 72 Profit per unit 80 70 Maximize M=80x+70y Carpentry: 6x + 3y ≤ 96 6x+ 3y+ u= 96 Finishing: x + y ≤ 18 x+ y + v= 18 Upholstery: 2x + 6y ≤ 72 2x+ 6y+ w =72 x ≥ 0 ; y ≥ 0 Initial Simplex Tableau X y u v w M R 6 3 1 0 0 0 96 1 1 0 1 0 0 18 2 6 0 0 1 0 72 -80 -70 0 0 0 1 0 Final Simplex Tableau X y u v w M R 1 0 1/3 -1 0 0 14 0 1 -1/3 2 0 0 4 0 0 4/3 -10 1 0 20 0 0 10/3 60 0 1 1400 This is a practice homework for these specific subjects: Setup and solve the LP problem using the Simplex method. Clearly label your answers and show all of your work. Maximize: z = 80x + 70y Subject To: 2x + 6y ≤ 72, constraint 1 6x + 3y ≤ 96, constraint 2 x + y ≤ 18, constraint 3 x ≥ 0 ; y ≥ 0 1. Give the final simplex tableau. 2. From the final simplex tableau give the solution to the problem and its dual. 3. Sensitivity analysis. o What is the range of feasibility for constraint 1? o If the resource for constraint 1 is increased by 1 what will be the new values of x and y? o If the resource for constraint 1 is increased by 1 what will be the new profit? o What is the shadow price corresponding to constraint 1? 4. Give the dual to the original problem. This is not a simplex tableau. Your answer should include Minimize . . . , subject to the constraints . . . . Your constraints should include the non-negativity constraints. 5. Solve the dual problem by converting it into a non-standard maximization problem. Do not solve by solving its dual. Are your answers the same as you found earlier? Explain why or why not. 6. Use the final simplex tableau to find the solution to the primal problem. Are your answers the same as you found earlier? Explain why or why not. 7. Given the following transition matrix A for a Markov process with states 1, 2, 3 and 4: 1 0 .6 0 0 1 0 .4 0 0 0 .6 0 0 .4 0 Find As the stead-state matrix for A. A. Is A an absorbing stochastic matrix? Explain why or why not. B. Find R and S C. Find (I − R)-1 D. -1 Find S(I − R) E. Use the previous results to find A S F. You can check your answers by raising A to a very high power.

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.