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Solved assignment problems – algorithms and flowcharts.
An algorithm is defined as sequence of steps to solve a problem (task) . The steps must be finite, well defined and unambiguous. Writing algorithm requires some thinking. Algorithm can also be defined as a plan to solve a problem and represents its logic. Note that an algorithm is of no use if it does not help us arrive at the desired solution
Algorithm characteristics
- It should have finite number of steps . No one can be expected to execute infinite number of steps.
- The steps must be in order and simple
- Each step should be defined clearly i.e. without un-ambiguity (without doubtfulness)
- Must include all required information
- Should exhibit at least one output
A flowchart is a pictorial (graphical) representation of an algorithm . A flowchart is drawn using different kinds of symbols. A symbol is used for a specific purpose. Each symbol has name.
| | |
An algorithm is defined as . | . | Set of instructions. Instruction is a command to the computer to do some task. |
Algorithm can also be defined as a plan to solve a problem and represents its logic. | A picture is worth of 1000 words. We can understand more from picture than words. | Implementation of Algorithm or flowchart |
Different algorithms have different performance characteristics to solve the same problem. Some algorithms are fast. Some are slow. Some occupy more memory space. Some occupy less memory space. Some are complex and some algorithms are simple.
Logically algorithm, flowchart and program are the same.
Q1 . Create a program to compute the volume of a sphere. Use the formula: V = (4/3) *pi*r 3 where pi is equal to 3.1416 approximately. The r is the radius of sphere. Display the result.
Q2 . Write a program the converts the input Celsius degree into its equivalent Fahrenheit degree. Use the formula: F = (9/5) *C+32.
Q3 . Write a program that converts the input dollar to its peso exchange rate equivalent. Assume that the present exchange rate is 51.50 pesos against the dollar. Then display the peso equivalent exchange rate.
Q4 . Write a program that converts an input inch(es) into its equivalent centimeters. Take note that one inch is equivalent to 2.54cms.
Q5 . Write a program that exchanges the value of two variables: x and y. The output must be: the value of variable y will become the value of variable x, and vice versa.
Q6 . Design a program to find the circumference of a circle. Use the formula: C=2πr, where π is approximately equivalent 3.1416.
Q7 . Write a program that takes as input the purchase price of an item (P), its expected number of years of service (Y) and its expected salvage value (S). Then outputs the yearly depreciation for the item (D). Use the formula: D = (P – S) Y.
Q8 . Swapping of 2 variables without using temporary (or 3 rd variable).
Q9 . Determine the most economical quantity to be stocked for each product that a manufacturing company has in its inventory: This quantity, called economic order quantity (EOQ) is calculated as follows: EOQ=2rs/1 where: R= total yearly production requirement S=set up cost per order I=inventory carrying cost per unit.
Q10 . Write a program to compute the radius of a circle. Derive your formula from the given equation: A=πr², then display the output.
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OPERATIONS RESEARCH
Lesson 9. solution of assignment problem.
Current course
Problem Questions with Answer, Solution - Exercise 10.2: Assignment problems(Hungarian Method) | 12th Business Maths and Statistics : Chapter 10 : Operations Research
Chapter: 12th business maths and statistics : chapter 10 : operations research, exercise 10.2: assignment problems(hungarian method).
Exercise 10.2
1. What is the Assignment problem?
2. Give mathematical form of assignment problem.
3. What is the difference between Assignment Problem and Transportation Problem?
4. Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.
5. A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.
Assign the programmers to the programme in such a way that the total computer time is least.
6. A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time each man would take to perform each task is given below
How should the tasks be allocated to subordinates so as to minimize the total man-hours?
7. Find the optimal solution for the assignment problem with the following cost matrix.
8. Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.
4. 46
5. 280
6. 41 Hours
7. 37
8. 12
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270+ Operations Research Solved MCQs
1. | |
A. | objective function |
B. | decision variable |
C. | constraints |
D. | opportunity cost |
Answer» A. objective function |
2. | |
A. | infeasible region |
B. | unbounded region |
C. | infinite region |
D. | feasible region |
Answer» D. feasible region |
3. | |
A. | outgoing row |
B. | key row |
C. | basic row |
D. | interchanging row |
Answer» C. basic row |
4. | |
A. | dummy |
B. | epsilon |
C. | penalty |
D. | regret |
Answer» B. epsilon |
5. | |
A. | ncwr |
B. | lcm |
C. | vam |
D. | hungarian |
Answer» D. hungarian |
6. | |
A. | head path |
B. | sub path |
C. | critical path |
D. | sub critical path |
Answer» C. critical path |
7. | |
A. | 7 |
B. | 10 |
C. | 18 |
D. | 8 |
Answer» B. 10 |
8. | |
A. | interfering float = total float – free float |
B. | total float =free float + independent float |
C. | total float ≥ free float ≥ independent float |
D. | free float = total float – head event slack |
Answer» B. total float =free float + independent float |
9. | |
A. | expected |
B. | pessimitic |
C. | optimistic |
D. | most likely |
Answer» C. optimistic |
10. | |
A. | processing order |
B. | idle time |
C. | processing time |
D. | elapsed time |
Answer» D. elapsed time |
11. | |
A. | physical |
B. | symbolic |
C. | deterministic |
D. | probabilistic |
Answer» C. deterministic |
12. | |
A. | physical |
B. | symbolic |
C. | deterministic |
D. | probabilistic |
Answer» D. probabilistic |
13. | |
A. | cpm and pert |
B. | assignment & transportation |
C. | game theory |
D. | decision theory & inventory models |
Answer» A. cpm and pert |
14. | |
A. | objective function |
B. | decision variables |
C. | constraints |
D. | opportunity cost |
Answer» B. decision variables |
15. | |
A. | objective function |
B. | decision variables |
C. | constraints |
D. | opportunity cost |
Answer» A. objective function |
16. | |
A. | objective function |
B. | variables |
C. | constraints |
D. | profit |
Answer» C. constraints |
17. | |
A. | infeasible |
B. | unbounded |
C. | improper |
D. | unknown |
Answer» A. infeasible |
18. | |
A. | less than or equal to |
B. | greater than or equal to |
C. | mixed |
D. | equal to |
Answer» D. equal to |
19. | |
A. | infeasible |
B. | infinite |
C. | unique |
D. | degenerate |
Answer» B. infinite |
20. | |
A. | key column |
B. | incoming column |
C. | important column |
D. | variable column |
Answer» A. key column |
21. | |
A. | vital element |
B. | important element |
C. | basic element |
D. | key element |
Answer» D. key element |
22. | |
A. | surplus |
B. | artificial |
C. | slack |
D. | additional |
Answer» C. slack |
23. | |
A. | null resource |
B. | scarce resource |
C. | abundant resource |
D. | zero resource |
Answer» B. scarce resource |
24. | |
A. | either zero or positive |
B. | either zero or negative |
C. | only positive |
D. | only negative |
Answer» A. either zero or positive |
25. | |
A. | vogel’s approximat ion method |
B. | nwcr |
C. | lcm |
D. | modi |
Answer» C. lcm |
26. | |
A. | infeasible solution |
B. | feasible solution |
C. | optimum solution |
D. | degenerate solution |
Answer» B. feasible solution |
27. | |
A. | infeasible solution |
B. | feasible solution |
C. | non degenerate solution |
D. | degenerate solution |
Answer» C. non degenerate solution |
28. | |
A. | vam |
B. | nwcr |
C. | modi |
D. | lcm |
Answer» A. vam |
29. | |
A. | balanced |
B. | unbalanced |
C. | infeasible |
D. | unbounded |
Answer» B. unbalanced |
30. | |
A. | vam |
B. | nwcr |
C. | modi |
D. | hungarian |
Answer» D. hungarian |
31. | |
A. | cost |
B. | regret |
C. | profit |
D. | dummy |
Answer» B. regret |
32. | |
A. | critical |
B. | sub-critical |
C. | best |
D. | worst |
Answer» A. critical |
33. | |
A. | tentative |
B. | definite |
C. | latest |
D. | earliest |
Answer» C. latest |
34. | |
A. | machines order |
B. | job order |
C. | processing order |
D. | working order |
Answer» C. processing order |
35. | |
A. | processing |
B. | waiting |
C. | free |
D. | idle |
Answer» D. idle |
36. | |
A. | objective function |
B. | decision variables |
C. | constraints |
D. | opportunity cost |
Answer» C. constraints |
37. | |
A. | less than |
B. | greater than |
C. | not greater than |
D. | not less than |
Answer» A. less than |
38. | |
A. | infeasible |
B. | infinite |
C. | unbounded |
D. | feasible |
Answer» D. feasible |
39. | |
A. | multiple constraints |
B. | infinite constraints |
C. | infeasible constraints |
D. | mixed constraints |
Answer» D. mixed constraints |
40. | |
A. | outgoing row |
B. | key row |
C. | interchanging row |
D. | basic row |
Answer» B. key row |
41. | |
A. | null resource |
B. | scarce resource |
C. | abundant resource |
D. | zero resource |
Answer» C. abundant resource |
42. | |
A. | unit price |
B. | extra price |
C. | retail price |
D. | shadow price |
Answer» D. shadow price |
43. | |
A. | either zero or positive |
B. | either zero or negative |
C. | only positive |
D. | only negative |
Answer» B. either zero or negative |
44. | |
A. | vogel’s approximat ion method |
B. | nwcr |
C. | lcm |
D. | modi |
Answer» A. vogel’s approximat ion method |
45. | |
A. | dummy |
B. | penalty |
C. | regret |
D. | epsilon |
Answer» D. epsilon |
46. | |
A. | there is no degeneracy |
B. | degeneracy exists |
C. | solution is optimum |
D. | problem is balanced |
Answer» A. there is no degeneracy |
47. | |
A. | dummy |
B. | non-critical |
C. | important |
D. | critical |
Answer» D. critical |
48. | |
A. | one |
B. | zero |
C. | highest |
D. | equal to duration |
Answer» B. zero |
49. | |
A. | optimistic |
B. | pessimistic |
C. | expected |
D. | most likely |
Answer» A. optimistic |
50. | |
A. | processing time |
B. | waiting time |
C. | elapsed time |
D. | idle time |
Answer» C. elapsed time |
51. | |
A. | invitees |
B. | players |
C. | contestants |
D. | clients |
Answer» B. players |
52. | |
A. | income |
B. | profit |
C. | payoff |
D. | gains |
Answer» C. payoff |
53. | |
A. | choices |
B. | strategies |
C. | options |
D. | actions |
Answer» B. strategies |
54. | |
A. | centre point |
B. | saddle point |
C. | main point |
D. | equal point |
Answer» B. saddle point |
55. | |
A. | 2 |
B. | 3 |
C. | 1 |
D. | 4 |
Answer» B. 3 |
56. | |
A. | parallel to x axis |
B. | parallel to y axis |
C. | passes through the origin |
D. | intersects both the axis |
Answer» A. parallel to x axis |
57. | |
A. | qualitative |
B. | quantitative |
C. | judgmental |
D. | subjective |
Answer» B. quantitative |
58. | |
A. | exact |
B. | earliest |
C. | latest |
D. | approximate |
Answer» B. earliest |
59. | |
A. | alternate |
B. | feasible solution |
C. | critical |
D. | sub-critical |
Answer» D. sub-critical |
60. | |
A. | degenerate |
B. | prohibited |
C. | infeasible |
D. | unbalanced |
Answer» B. prohibited |
61. | |
A. | Research |
B. | Decision – Making |
C. | Operations |
D. | None of the above |
Answer» B. Decision – Making |
62. | |
A. | J.F. McCloskey |
B. | F.N. Trefethen |
C. | P.F. Adams |
D. | Both A and B |
Answer» D. Both A and B |
63. | |
A. | 1950 |
B. | 1940 |
C. | 1978 |
D. | 1960 |
Answer» B. 1940 |
64. | |
A. | Civil War |
B. | World War I |
C. | World War II |
D. | Industrial Revolution |
Answer» C. World War II |
65. | |
A. | Battle field |
B. | Fighting |
C. | War |
D. | Both A and B |
Answer» D. Both A and B |
66. | |
A. | Morse and Kimball (1946) |
B. | P.M.S. Blackett (1948) |
C. | E.L. Arnoff and M.J. Netzorg |
D. | None of the above |
Answer» A. Morse and Kimball (1946) |
67. | |
A. | E.L. Arnoff |
B. | P.M.S. Blackett |
C. | H.M. Wagner |
D. | None of the above |
Answer» C. H.M. Wagner |
68. | |
A. | C. Kitte |
B. | H.M. Wagner |
C. | E.L. Arnoff |
D. | None of the above |
Answer» A. C. Kitte |
69. | |
A. | Scientists |
B. | Mathematicians |
C. | Academics |
D. | All of the above |
Answer» A. Scientists |
70. | |
A. | Economists |
B. | Administrators |
C. | Statisticians and Technicians |
D. | All of the above |
Answer» D. All of the above |
71. | |
A. | System Orientation |
B. | System Approach |
C. | Interdisciplinary Team Approach |
D. | none |
Answer» D. none |
72. | |
A. | Answers |
B. | Solutions |
C. | Both A and B |
D. | Decisions |
Answer» C. Both A and B |
73. | |
A. | Quality |
B. | Clarity |
C. | Look |
D. | None of the above |
Answer» A. Quality |
74. | |
A. | Scientific |
B. | Systematic |
C. | Both A and B |
D. | Statistical |
Answer» C. Both A and B |
75. | |
A. | Two or more |
B. | One or more |
C. | Three or more |
D. | Only One |
Answer» B. One or more |
76. | |
A. | Conducting experiments on it |
B. | Mathematical analysis |
C. | Both A and B |
D. | Diversified Techniques |
Answer» C. Both A and B |
77. | |
A. | Policies |
B. | Actions |
C. | Both A and B |
D. | None of the above |
Answer» C. Both A and B |
78. | |
A. | Science |
B. | Art |
C. | Mathematics |
D. | Both A and B |
Answer» D. Both A and B |
79. | |
A. | Scientific Models |
B. | Algorithms |
C. | Mathematical Models |
D. | None of the above |
Answer» C. Mathematical Models |
80. | |
A. | Quailing Theory |
B. | Waiting Line |
C. | Both A and B |
D. | Linear Programming |
Answer» D. Linear Programming |
81. | |
A. | Inventory Control |
B. | Inventory Capacity |
C. | Inventory Planning |
D. | None of the above |
Answer» C. Inventory Planning |
82. | |
A. | Inventory Control |
B. | Inventory |
C. | Inventory Planning |
D. | None of the above |
Answer» B. Inventory |
83. | |
A. | Game Theory |
B. | Network Analysis |
C. | Decision Theory |
D. | None of the above |
Answer» C. Decision Theory |
84. | |
A. | Game Theory |
B. | Network Analysis |
C. | Decision Theory |
D. | None of the above |
Answer» B. Network Analysis |
85. | |
A. | Simulation |
B. | Integrated Production Models |
C. | Inventory Control |
D. | Game Theory |
Answer» A. Simulation |
86. | |
A. | Search Theory |
B. | Theory of replacement |
C. | Probabilistic Programming |
D. | None of the above |
Answer» B. Theory of replacement |
87. | |
A. | Probabilistic Programming |
B. | Stochastic Programming |
C. | Both A and B |
D. | Linear Programming |
Answer» C. Both A and B |
88. | |
A. | Programme Evaluation |
B. | Review Technique (PERT) |
C. | Both A and B |
D. | Deployment of resources |
Answer» C. Both A and B |
89. | |
A. | Schedule |
B. | Product Mix |
C. | Both A and B |
D. | Servicing Cost |
Answer» C. Both A and B |
90. | |
A. | Men and Machine |
B. | Money |
C. | Material and Time |
D. | All of the above |
Answer» D. All of the above |
91. | |
A. | Three |
B. | Four |
C. | Five |
D. | Two |
Answer» A. Three |
92. | |
A. | Sequencing |
B. | Allocation Models |
C. | Queuing Theory |
D. | Decision Theory |
Answer» B. Allocation Models |
93. | |
A. | Linear Programming Technique |
B. | Non – Linear Programming Technique |
C. | Both A and B |
D. | None of the above |
Answer» C. Both A and B |
94. | |
A. | Deterministic Models |
B. | Probabilistic Models |
C. | Both A and B |
D. | None of the above |
Answer» A. Deterministic Models |
95. | |
A. | Deterministic Models |
B. | Probabilistic Models |
C. | Both A and B |
D. | None of the above |
Answer» B. Probabilistic Models |
96. | |
A. | Iconic Models |
B. | Analogue Models |
C. | Symbolic Models |
D. | None of the above |
Answer» A. Iconic Models |
97. | |
A. | Optimum |
B. | Perfect |
C. | Degenerate |
D. | None of the above |
Answer» A. Optimum |
98. | |
A. | Research |
B. | Operation |
C. | Both A and B |
D. | None of the above |
Answer» B. Operation |
99. | |
A. | Decision Theory |
B. | Simulation |
C. | Game Theory |
D. | None of the above |
Answer» B. Simulation |
100. | |
A. | Queuing Theory |
B. | Decision Theory |
C. | Both A and B |
D. | None of the above |
Answer» A. Queuing Theory |
Done Reading?
- Question and answers in Operations Research,
- Operations Research multiple choice questions and answers,
- Operations Research Important MCQs,
- Solved MCQs for Operations Research,
- Operations Research MCQs with answers PDF download
Excel Practice Exercises PDF with Answers
To solve the following exercises, you will need to know about the SUM , AVERAGE , IF , VLOOKUP , INDEX , MATCH , ROUNDUP , UNIQUE , COUNTIF , LEFT , SEARCH , MID , RIGHT , LEN , FIND , SUBSTITUTE , AND , and SUMIF functions and the Data Bars feature of Excel. You can use Excel 2010 or later, except for the UNIQUE function, which is only available in Excel 2021 .
Download the Practice Files
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Problem Overview
Here is a snapshot of the first two problems. The solutions to all problems are given in a separate sheet.
- Exercise 01 – Class Performance Evaluation . You will find these values –
- The total number for each student,
- Their average on those subjects,
- Based on the average score, you will return a GPA. For GPA calculation, less than 60 is B and higher is A .
- You need to find the employee salary in the lookup table on the right side.
- Exercise 03 – Lookup Values (Any Direction) .
- Here your task is the same as the second task. However, this time the lookup range is on the right side. Therefore, you cannot use the VLOOKUP function here.
- You will need to round the sales generated values in this exercise.
- You will need to add the first name and last name.
- Your task is to create a Data Bar for the salary values and hide the salary values.
- Firstly, you need to find the unique values in a list of names.
- Then, you will find how many times that value occurred in that lis
- You need to separate the three parts of a name from a given list.
- You will need to find the total sales for a particular country.
- Your objective is to ensure that users cannot type less than 0 in a column.
- Your target is to determine whether a date is between two dates or not.
Here is a screenshot of the solutions to the first two problems.
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Advanced Excel Exercises with Solutions PDF
IMAGES
COMMENTS
e minimisation problem.3. The assignment problem wherein the number of rows is not equal to the number of columns is said t. be an unbalanced problem. Such a problem is handled by introducing dummy row(s) if the number of rows is less than the number of columns and dummy column(s) if the number of columns is le.
introduction to assignment problem matrix form of assignenmt problem mathematical formulation of an assignment problem difference between transportation problem and assigment problem assigment algorithm (or) hungarian method example of assigment problems question to answer mcq questions with answer k.bharathi,scsvmv. assignment problem 2 / 55
Solve the following assignment problem. Solution: Since the number of columns is less than the number of rows, given assignment problem is unbalanced one. To balance it , introduce a dummy column with all the entries zero. The revised assignment problem is. Here only 3 tasks can be assigned to 3 men.
Problem 4. Job shop needs to assign 4 jobs to 4 workers. The cost of performing a job is a function of the skills of the workers. Table summarizes the cost of the assignments. Worker1 cannot do job3, and worker 3 cannot do job 4. Determine the optimal assignment using the Hungarian method. Job.
8.1 Introduction. An assignment problem is a particular case of transportation problem in which a number of operations are to be assigned to an equal number of operators, where each operator performs only one operation. The objective is to minimize overall cost or to maximize the overall profit for a given assignment schedule.
Hungarian method for assignment problem Step 1. Subtract the entries of each row by the row minimum. Step 2. Subtract the entries of each column by the column minimum. Step 3. Make an assignment to the zero entries in the resulting matrix. A = M 17 10 15 17 18 M 6 10 20 12 5 M 14 19 12 11 15 M 7 16 21 18 6 M −10
Module 4: Transportation Problem and Assignment problem. Transportation problem is a special kind of Linear Programming Problem (LPP) in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the sources and destination respectively such that the total cost of transportation is minimized.
Program. An algorithm is defined as sequence of steps to solve a problem (task). A flowchart is pictorial (graphical) representation of an algorithm. Set of instructions. Instruction is a command to the computer to do some task. Algorithm can also be defined as a plan to solve a problem and represents its logic. A picture is worth of 1000 words.
Exercise 17 shows that the number of iterations is O(n2). To compare the Hungarian method to the exhaustive search method mentioned above, suppose that each iteration can be performed in one second. Then an assignment prob-lem with n = 30 can be solved in at most 302 = 900 seconds, or 15 minutes of computer time.
• Solve the assignment problem using Hungarian method. • Analyze special cases in assignment problems. Writing of an assignment problem as a Linear programming problem Example 1. Three men are to to be given 3 jobs and it is assumed that a person is fully capable of doing a job independently. The following
Step 3. Draw lines through appropriate rows and columns so that all the zero entries of the cost matrix are covered and the minimum number of such lines is used. Step 4. Test for Optimality: (i) If the minimum number of covering lines is n, an optimal assignment of zeros is possible and we are finished.
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THE HUNGARIAN METHOD FOR THE ASSIGNMENT. PROBLEM'. H. W. Kuhn. Bryn Y a w College. Assuming that numerical scores are available for the perform- ance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the. n scores so obtained is as large as possible.
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The assignment problem can be solved by the following four methods: a) Complete enumeration method. b) Simplex Method. c) Transportation method. d) Hungarian method. 9.2.1 Complete enumeration method. In this method, a list of all possible assignments among the given resources and activities is prepared.
1. What is the Assignment problem? 2. Give mathematical form of assignment problem. 3. What is the difference between Assignment Problem and Transportation Problem? 4. Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below.
Analysing an assignment question For every assignment you need to : • Understand the question • Brainstorm ideas • Read enough relevant, reliable information to answer the question properly. • Structure your assignment • Present your main ideas or arguments and • Support your main ideas or arguments • Edit your writing for coherence and unity • Proofread for grammar ...
Step 4. Making the optimal Assignment: Select the a row with only one '0' in it. Make an Assignment by marking' ' around '0' of this row. After making assignment cross 'X' out all other '0's in the corresponding column. Repeat this step for all remaining rows that fulfil 'only one zero' condition.
Intermediate Microsoft Excel Worksheet: Practice 1. Objectives: The Learner will be able to: Enter data into a Spreadsheet. Use AutoFill with labels, data, and formulas. Format Cell Borders and Contents. Calculate the total across the rows. Calculate the total for each column. Use Conditional Formatting.
Assignment Question 9. Download Solution PDF. Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the machines for each of the jobs, are given in the table.
When a maximization assignment problem is converted in minimization problem, the resulting matrix is called matrix. ... Question and answers in Operations Research, Operations Research multiple choice questions and answers, ... Solved MCQs for Operations Research, Operations Research MCQs with answers PDF download * Related Topics. Computer ...
Exercise 04 - Rounding Values. You will need to round the sales generated values in this exercise. Exercise 05 - Joining Two Strings . You will need to add the first name and last name. Exercise 06 - Conditional Formatting . Your task is to create a Data Bar for the salary values and hide the salary values. Exercise 07 - Counting Unique ...