homework help

Blending Models

Personalized homework help for all major subjects.

Order confidently with our risk free, 14-day money-back guarantee.

  • ✔️ No sign-up required
  • | 🔒 100% Confidential

Our Expert Writers

We proudly boast a team of expert professionals with verified academic credentials, selected for their proven skills and flexibility through a strict process.

Engage with experts from the top universities across the globe.

Get Homework Help Instantly

Say goodbye to homework stress! 📚 Just share your details and we’ll whip up an affordable quote in no time – often within 15 minutes.

Get started now for FREE!

Submit Your Homework

Let our experts help you with your college homework

In order to determine the most favourable integration of various components that are required to be mixed to produce a final product is the reason of preparing blending models. This model is widely used in many industrial sectors. Few areas of its blending application are:

  • Teas
  • Petroleum products
  • Coffees
  • Feed-mixes to be utilised for agricultural purpose
  • Fertilisers and much more.

A reduction in the blending cost is the aim of these models. If common constraints are taken into account, it includes 3 part.

  • Demanded size of blends
  • Ingredients which are available in finite quantity
  • Technological requirements

Workings of the model can be explained with the help of an example.

Example

Suppose, there are 3 final blends of gasoline and4 petroleum products which are required to be blended by a small refinery. There are no accurate blending formulas, and in addition to it, there few limitations that are required to be abided in the entire blending process. Few of the limitations are:

  • The precise percentage of component 1 should be 35% of blend 3.
  • The constituting percentage of component 2 should not exceed 40% of blend 1’s volume.
  • On combining component 2 and 4, the blending percentage should be a minimum of 60% of blend 1’s volume.
  • 20% of blend 2 should be the constituent of component 3.

Component 2 and 3 is scarcely available in an amount of 1600 Kilolitres and 200 Kilolitres. 6000 Kilolitres in totality is demanded to be blended by the production manager. An estimated blending amount that can be finally produced out of the total quantity is 2500 Kilolitres.After the final blends are sold at a wholesale price, the amount stands to be Rs. 12, Rs. 18, and Rs. 20 for per litre.

The cost of components utilised in the blends are Rs. 10, Rs. 12, Rs. 13 and Rs. 15 per litres. Now the volume of each component is required to be found out in litres for every final blend in the course of production. The motive of this problem is to find the answer by magnifying its total profit contribution.

Solution

Component I utilised in the find blend J be represented as XIJ.

Profit contribution in totality = Total earnings from all 3 blends – Costing of all 4 components in totality

= Profit blend 1 + Profit blend 2 + Profit blend 3 – (cost of components I, 2, 3 and 4)

= Rs (20 + 18 + 12) – Rs (10 + 15 + 12 + 13)

 

The objective function stands at,

Z= [20 (x11 +x21 +x31+x41) + 18 (x12 +x22+x32+x42) + 12 (x13+x23+x33 +x43)] – [10 (x11+ x12+ x13) + 15 (x21+ x22+ x23) + 12 (x31+ x32+ x33) + 13 (x41+ x42+ x43)]

Or

Z = 10 x11+ 8 x12+ 2 x13+ 5 x21+ 3 x22– 3x23 + 8 x31+ 6 x32+ 0 x33+ 7 x41+ 5 x41-x43.

 

The constraints are,

  1. 6000 Kilolitres should be the total production run.

x11+ x12+ x13+ x21+ x22+ x23+ x31+ x32 + x33 + x41+ x42+ x43= 6000,000 litres

  1. Limitations in the recipe are:
  • The constituting percentage of component 2 should not exceed 40% of blend 1’s volume.

X21≤ 0·4 (x11 +x21+x31+x41)

Or

-0.4 x11 +0.6 x21-0.4x31-0.4 x41≤ 0

  • 20% of blend 2 should be the constituent of component 3.

x32 ≥0.20 (x12+ x22+ x32 + x42)

or

–0.2 x12– 2·0 x22+ 0.8 x32–0.20 x42 ≥ 0

  • The precise percentage of component 1 should be 35% of blend 3.

x13= 0.35 (x13+ x23+ x33 + x43)

Or

0.65 x13– 0.35 x23– 0.35 x33 – 0.35 x43= 0

  • On combining component 2 and 4, the blending percentage should be a minimum of 60% of blend 1’s volume.

x21+ x41 ≥0.6 (x11+ x21+ x31+ x41 )

Or

-0.6 x11+ 0·4 x21-0·6x31 +0·4 x41≥ 0

  • Representation of scarcely limited components 2 and 3 can be showed by this equation.

x21+ x22+ x23 ≤  1600,000

x31+ x32 + x33 ≤1200,000

  • Minimum production requirement constraint in final blend 1 can be represented as

x11 +x21 +x31 +x41 ≥ 2500,000

The complete linear programming model is,

Maximise

Z= 10 x11+ 8 x12+ 2 x13+ 5 x21+ 3 x22-3x23+ 8 x31+ 6x32 – 0 x33+ 7 x41+ 5 x42– x43

Subject to

x11+ x12+ x13+ x21+ x22+ x23+ x31+ x32+ x33+ x41 + x42+ x43= 6000,000

-0.4 x11+ 0.6 .x21 – 0.4 x31 – 0.4 -x41 ≤ 0

-0.2x12– 0·20 x22+0·8 x32-0·20 x42≥ 0

+0.65 x13– 0.35x23– 0.35x33– 0.35x43=0

-0·6 x11+0·4x21-0·6 x31+0·4x41 ≥0

x21+ x22+ x23 ≤1600,000

x31+ x32+ x33 ≤1200,000

x11 +x21 +x31+x41≤ 2500,000

x11, x12,x13,x21, x22, x23, x31, x32, x33, x41, x42, x43 ≥0

 

Links of Previous Main Topic:-

Links of Next Finance Topics:-

Your Price: $11.00 $10.00

Pricing may change based on requirements

Descriptive text for the image

Get Homework Help In

Maths and Statistics

Science

Humanities & Arts

l

Essay Writing

How Our Homework Service Works

FAQ number 1

Share your requirements

FAQ number 2

Make secure payment

FAQ number 3

Get homework answers

FAQ - Frequently Asked Questions

Discover quick answers in our FAQ, covering the most common customer questions about our homework help service.

Is your homework service confidential?

M
L

Absolutely! Confidentiality is one of the basic guarantees of our service at MyHomeworkHelp.com.

When our customers make their homework orders, they know their information remains 100% confidential.

Even your homework writer will not be provided with your personal details. So, when you hire a professional homework helper on our website, rest assured that your information will remain private and safe.

For a comprehensive understanding of how we protect your privacy, please refer to our Privacy Policy.

Who will help me with my homework?

M
L

We work with subject experts from all over the world. We hire them with the help of complex tests in the disciplines of their expertise. We also verify the IDs and academic transcripts of our homework writers to be sure that our experts have a bachelor's or master’s or a PhD degree. This is how we can be sure of the proficiency of our panel of experts who will help you with your homework.

Is it legal to ask for help with homework?

M
L

Seeking homework help is perfectly fine and shows your proactive approach to overcoming challenges. But it's important to use our homework service to enhance your understanding, not to replace your own efforts.

Our homework service offers original solutions for personal use, including:

  • Generating ideas or arguments for your research.
  • Deepening your subject comprehension.
  • Direct citation, with proper referencing.

However, it's crucial to avoid plagiarism by not submitting our work as your own. Make sure to check your institution's academic integrity policies before using our services. Our goal is to support your educational journey in a responsible and beneficial way. Refer our honor code for more details.

Is myhomeworkhelp.com legit?

M
L

Yes, myhomeworkhelp.com is completely legitimate. We've been successfully connecting students with top experts worldwide since 2012, offering direct, secure communication for a seamless learning experience. With over thousands of students helped and a commitment to innovative, effective education tools, we're dedicated to making learning easier and more accessible for everyone.

You can read our reviews here on Trustpilot and Sitejabber (Independent, verified reviews from buying customers) like you!

Is there a possibility of plagiarism in my completed order?

M
L

Unlike our competitors who use cheap and ineffective in -house plagiarism software, MyHomeworkHelp.com uses credible software to check your homework solution originality. We guarantee that your paper will pass TurnItIn checks with a low percentage of similarity. In addition, we also check submitted papers for ai-content using Originality.ai.

You will receive a complemantary plagiarism free report with your completed order.

What makes you one of the best homework help website?

M
L

We are not number 1 (yet!). We're an independent, bootstrapped business standing up to Big EdTech for last 12 years. So it means a lot that folks like you are willing to consider our services for your educational needs.

Myhomework Help is recognized as one of the premier websites for homework answers for three key reasons.

  1. Firstly, we pride ourselves on the expertise and qualifications of our tutors/experts, who are selected through a rigorous vetting process to ensure they can provide best academic assistance across a wide range of subjects.
  2. Secondly, our response time to student inquiries is fast (as early as few minutes), reflecting our understanding of the importance of timely support in an academic setting.
  3. Lastly, we keep our pricing very student friendly. Our aim is to provide the best learning experience to students like yourself without burning a hole in your pockets.