homework help

Unbalanced Problems

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

Establish whether the assignment problems are balanced one or not. This means to check the number of rows to be equal to number of columns. If this happens, then we will proceed as discussed earlier. If this is not achieved, then we have to add dummy row/ column as per the case to balance the problem by allotting zeros (0).

Example 6.1:

A department with four subordinates had to perform four tasks. Each subordinate differs in its performance and efficiency. The tasks also differ in its intrinsic difficulty. The estimated time taken by each subordinate to perform each task has been given in the following matrix.

Tasks                                       Men

                        E                      F                      G                      H

A                      18                    26                    17                    11

B                      13                    18                    14                    26

C                      38                    19                    18                    15

D                      19                    26                    24                    10

How to allot the task to each subordinate to get the minimized total man hours?

Solution:

Step 1:

Subtract the smallest value from each row to the corresponding row to reduce the matrix as follow (subtract 11 from row one, 13 from row two, 15 from third row and 10 from fourth row).

7          15        6          0

0          15        1          3

23        4          3          0

9          16        14        0

Step 2:

Subtract the smallest value from each column to the corresponding column to reduce the matrix as follow (subtract 0 from column one, 4 from column two, 1 from third column and 0 from fourth column).

7          11        5          0

0          11        0          13

23        0          2          0

9          12        13        0

Step 3:

Start from the first row, we put asquare to first zero in each row and cross our all other zeroes in the same row. By doing so, we;

7          11        5          0

0          11        0          13

23        0          2          0

9          12        13        0

Note:

Since row two has two zeros, we will arbitrarily choose this to made assignment to zero in the column one and put a square around it. Moreover, column three and four do not have any assignments.

Step 4:

  1. Tick the row four as it does not have any assignment. In the 4th column and 4th row, there is a zero. So, we will tick this 4th
  2. In the row first of ticked column i.e. 4th column, there is an assignment made. Thus, first row will be ticked.
  3. Draw straight lines through all the marked columns and unmarked rows.

Following matrix highlights the above steps:

7          11        5          0         

0          11        0          13

23        0          2          0

9          12        13        0         

Step 5:

Whether this solution is optimal or not? Of course not! This is because there are only 3 lines drawn and it is less than order of the matrix (4). Hence, we have to generate new zeros to increase the minimum number of lines to make it an optimal solution.

Step 6:

Find out the smallest element that is not covered by any of these lines. It is the value ‘5’. Subtract this value from all uncovered elements and add to all elements that are lying at the intersection of two lines. Thus, we get the following matrix;

2          6          0          0

0          11        0          18

23        0          2          5

4          7          8          0

Step 7:

Repeat Step 3 to reduce the matrix row-wise to make an assignment to a single zero, we get;

E          F         G          H

A          2          6          0          0

B          0          11        0          18

C          23        0          2          5

D          4          7          8          0

Result:

Now, we can see that an optimal solution is obtained. Each column and each row have only one assignment. Thus, optimum assignment will be;

A→G, B→E, C→F, D→H

Therefore,

Minimum total time taken for this assignment problem would be obtained by-

17 + 13 + 19 + 10 = 59 man-hours

Example 6.2:

A marketing manager has to cover 5 districts with his 5salesmen. Considering the capability of each salesman and nature of each district, its manager has estimated that sales per month (in hundred rupees) would be as follows:

Salesman                                                        Districts

                        A                      B                      C                      D                      E

1                      30                    38                    40                    28                    40

2                      40                    24                    28                    21                    36

3                      41                    27                    33                    30                    37

4                      22                    38                    41                    36                    36

5                      29                    33                    40                    35                    39

Find out the assignment of 5 salesmen to 5 districts to get maximum sales.

Solution:

This is a maximization problem needs to convert into a minimization problem. It can be done by subtracting all elements with the largest element i.e. 41. Thus, the following matrix can be obtainedby reducing it with 41;

11        3          1          13        1

1          17        13        20        5

0          14        8          11        4

19        3          0          5          5

12        8          1          6          2

Step 1:

Subtracting the smallest value of each row with every other element of the same row, we get;

10        2          0          12        0

0          16        12        19        4

0          14        8          11        4

19        3          0          5          5

11        7          0          5          1

Step 2:

Subtracting the smallest value of each column with every other element of the same column, we get;

11        3          1          13        1

1          17        13        20        5

0          14        8          11        4

19        3          0          5          5

12        8          1          6          2

Step 3:

Start from the row one to make the assignment a single zero. Cross out all the other zeros, then we get;

10        0          0          7          0

0          14        12        14        4

0          12        8          6          4

19        1          0          0          5

11        5          0          0          1

Step 4:

Here 3rd row and 4th column do not have any assignment. Now, draw the minimum numbers of straight lines horizontally and vertically to cover all the zeroes, we get;

10        0          0          7          0

0          14        12        14        4

0          12        8          6          4

19        1          0          0          5

11        5          0          0          1

We find that number of lines (i.e. 4) is less than order of matrix (i.e. 5). This means the solution is not optimal.

Step 5:

The value 4 is the least uncovered element which is subtracted from all uncovered elements and added to the intersection of each element. Thus, the matrix reduces to;

A          B          C          D          E

1          10        0          0          7          0

2          0          14        12        14        4

3          0          8          4          2          0

4          23        1          0          0          5

5          15        5          0          0          1

Result:

The optimum solution will be;

1 →B, 2 →A, 3 →E, 4 →C, 5 →D

i.e., 38 + 40 + 37 + 41 + 35 = 191

Thus, the maximum sale would be Rs. 19,100.

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.