Prepare for your exams
Get points
Guidelines and tips
Sell on Docsity
Docsity AI

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Docsity AI

Log in Sign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

optimization techniques, Exams of Operational Research

Middlesex University Operational Research

good notes of operational rearch

Typology: Exams

2016/2017

Uploaded on 03/23/2017

rishabh-jain 🇬🇧

1 document

1 / 1

This page cannot be seen from the preview

Don't miss anything!

Department of Mathematics

Tutorial/Assignment Sheet (Unit- I - B )

Subject Name: OPTIMIZATION TECHNIQUES Subject Code: CSE-6002

Simplex Method and Big-M Method

1. Max z = 22x1 + 30 x2 + 25x3 subject to

2x1 + 2x2 ≤ 100, 2x1 + x2 + x3 ≤ 100 , x1 + 2x2 + 2x3 ≤ 100 , x1 , x2, x3 ≥0

Ans: 𝒙𝟏=𝟏𝟎𝟎

𝟑, 𝒙𝟐=𝟓𝟎

𝟑, 𝒙𝟑=𝟓𝟎

𝟑, 𝒁𝒎𝒂𝒙 =𝟏𝟔𝟓𝟎

2. Max z = 4x1 + 3x2 subject to

x1 + x2 ≤ 50, x1 + 2x2 ≥ 80, 3x1 + 2x2 ≥ 140, x1, x2 ≥ 0

Ans: Infeasible Solution

3. Max 𝑧 = 3𝑥1+ 4𝑥2, Subject to

𝑥1− 𝑥2≤ 1 , −𝑥1+ 𝑥2≤ 2 , 𝑥1, 𝑥2≥ 0.

Ans: Unbounded Solution

4. Max 𝑧 = 7𝑥1+ 𝑥2+ 2𝑥3+ 7, Subject to

𝑥1+ 𝑥2− 2𝑥3≤10 , 4𝑥1+ 𝑥2+ 𝑥3≤20 , 𝑥1, 𝑥2, 𝑥3≥ 0.

Ans: 𝒙𝟏= 𝟎, 𝒙𝟐= 𝟎, 𝒙𝟑=𝟐𝟎, 𝒁𝒎𝒂𝒙 =𝟒𝟕

5. Min 𝑧 = 60𝑥1+80𝑥2, Subject to

𝑥1+ 𝑥2=500 , −𝑥1≥ −400 , 𝑥2≥200 𝑥1, 𝑥2≥ 0.

Ans: 𝒙𝟏=𝟑𝟎𝟎, 𝒙𝟐=𝟐𝟎𝟎, 𝒁𝒎𝒊𝒏 =𝟑𝟒𝟎𝟎

6. Max 𝑧 = 4𝑥1+10𝑥2, Subject to

2𝑥1+ 𝑥2≤50 , 2𝑥1+ 5𝑥2≤100 , 2𝑥1+ 3𝑥2≤90, 𝑥1, 𝑥2≥ 0.

Ans: Two optimal Solution a) 𝒙𝟏= 𝟎, 𝒙𝟐=𝟐𝟎, 𝒁𝒎𝒂𝒙 =𝟐𝟎𝟎

b) 𝒙𝟏=𝟕𝟓

𝟒, 𝒙𝟐=𝟐𝟓

𝟐, 𝒁𝒎𝒂𝒙 =𝟐𝟎𝟎

7. Min 𝑧 = 12𝑥1+20𝑥2, Subject to

6𝑥1+ 8𝑥2≥100 , −7𝑥1−12𝑥2≤ −400 , 𝑥1, 𝑥2≥ 0.

Ans: 𝒙𝟏=𝟏𝟓, 𝒙𝟐=𝟓

𝟒, 𝒁𝒎𝒊𝒏 =𝟐𝟎𝟓

Discover Exams of Operational Research Middlesex University

Partial preview of the text

Download optimization techniques and more Exams Operational Research in PDF only on Docsity!

Department of Mathematics Tutorial/Assignment Sheet (Unit- I - B ) Subject Name: OPTIMIZATION TECHNIQUES Subject Code: CSE- Simplex Method and Big-M Method

Max z = 22x 1 + 30 x 2 + 25x 3 subject to 2x 1 + 2x 2 ≤ 100, 2x 1 + x 2 + x 3 ≤ 100 , x 1 + 2x 2 + 2x 3 ≤ 100 , x 1 , x 2 , x 3 ≥ Ans: 𝒙𝟏 = 𝟏𝟎𝟎 𝟑

𝟓𝟎 𝟑

Max z = 4x 1 + 3x 2 subject to x 1 + x 2 ≤ 50, x 1 + 2x 2 ≥ 80, 3x 1 + 2x 2 ≥ 140, x 1 , x 2 ≥ 0 Ans: Infeasible Solution
Max 𝑧 = 3𝑥 1 + 4𝑥 2 , Subject to 𝑥 1 − 𝑥 2 ≤ 1 , −𝑥 1 + 𝑥 2 ≤ 2 , 𝑥 1 , 𝑥 2 ≥ 0. Ans: Unbounded Solution
Max 𝑧 = 7𝑥 1 + 𝑥 2 + 2𝑥 3 + 7, Subject to 𝑥 1 + 𝑥 2 − 2𝑥 3 ≤ 10 , 4𝑥 1 + 𝑥 2 + 𝑥 3 ≤ 20 , 𝑥 1 , 𝑥 2 , 𝑥 3 ≥ 0. Ans: 𝒙𝟏 = 𝟎, 𝒙𝟐 = 𝟎, 𝒙𝟑 = 𝟐𝟎, 𝒁𝒎𝒂𝒙 = 𝟒𝟕
Min 𝑧 = 60𝑥 1 + 80𝑥 2 , Subject to 𝑥 1 + 𝑥 2 = 500 , −𝑥 1 ≥ −400 , 𝑥 2 ≥ 200 𝑥 1 , 𝑥 2 ≥ 0. Ans: 𝒙𝟏 = 𝟑𝟎𝟎, 𝒙𝟐 = 𝟐𝟎𝟎, 𝒁𝒎𝒊𝒏 = 𝟑𝟒𝟎𝟎
Max 𝑧 = 4𝑥 1 + 10𝑥 2 , Subject to 2𝑥 1 + 𝑥 2 ≤ 50 , 2𝑥 1 + 5𝑥 2 ≤ 100 , 2𝑥 1 + 3𝑥 2 ≤ 90, 𝑥 1 , 𝑥 2 ≥ 0. Ans: Two optimal Solution a) 𝒙𝟏 = 𝟎, 𝒙𝟐 = 𝟐𝟎, 𝒁𝒎𝒂𝒙 = 𝟐𝟎𝟎 b) 𝒙𝟏 = 𝟕𝟓 𝟒

𝟐𝟓 𝟐

Min 𝑧 = 12𝑥 1 + 20𝑥 2 , Subject to 6𝑥 1 + 8𝑥 2 ≥ 100 , −7𝑥 1 − 12𝑥 2 ≤ −400 , 𝑥 1 , 𝑥 2 ≥ 0. Ans: 𝒙𝟏 = 𝟏𝟓, 𝒙𝟐 = 𝟓 𝟒

optimization techniques, Exams of Operational Research

Related documents

Partial preview of the text

Download optimization techniques and more Exams Operational Research in PDF only on Docsity!