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The linear programming is used for optimization problems which satisfy the following conditions:
1. Objective function is expressed as a linear function of variables.
2. Resources are unlimited.
3. The decision variables are interrelated and non-negative.
1. Objective function is expressed as a linear function of variables.
2. Resources are unlimited.
3. The decision variables are interrelated and non-negative.
Which of these statements is/are correct?
- a)1,2 and 3
- b)2 and 3 only
- c)1 only
- d)1 and 3 only
Correct answer is option 'D'. Can you explain this answer?
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The linear programming is used for optimization problems which satisfy...
LP is used for optimization problems having limited resource. Unlimited resources have nothing to do with optimization.
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The linear programming is used for optimization problems which satisfy...
Linear Programming for Optimization Problems
Linear Programming is a mathematical technique used for optimization problems that satisfy the following conditions:
1. Objective function is expressed as a linear function of variables.
2. Resources are limited.
3. The decision variables are interrelated and non-negative.
Explanation of Correct Answer
The correct answer is option 'D', which means that statements 1 and 3 are correct.
1. Objective function is expressed as a linear function of variables: This means that the objective function can be represented as a linear combination of decision variables, where the coefficients of the variables are constants. For example, if we want to maximize profit, then the objective function can be represented as:
Maximize P = 10x + 20y
Where x and y are decision variables representing the quantities of two products.
2. Resources are limited: This statement is incorrect because resources are not unlimited in linear programming. In fact, the constraints of the problem represent the limited resources available.
For example, if we have a certain amount of raw material available for production, then the constraint can be represented as:
2x + 3y ≤ 500
Where x and y are decision variables representing the quantities of two products, and 500 is the limit of available raw material.
3. The decision variables are interrelated and non-negative: This statement is correct because the decision variables are related to each other and cannot be negative. In other words, the value of one variable depends on the value of other variables and all variables must have a non-negative value.
For example, if we want to minimize cost, then the constraints can be represented as:
x + y ≥ 100
2x + 3y ≥ 200
x ≥ 0, y ≥ 0
Where x and y are decision variables representing the quantities of two products, and the constraints represent the minimum production requirements and non-negativity condition.
Conclusion
Linear Programming is a powerful optimization tool that can be used to solve complex problems in various fields such as engineering, economics, and management. By formulating a problem as a linear program, we can find the optimal solution that satisfies the given constraints and objectives.
Linear Programming is a mathematical technique used for optimization problems that satisfy the following conditions:
1. Objective function is expressed as a linear function of variables.
2. Resources are limited.
3. The decision variables are interrelated and non-negative.
Explanation of Correct Answer
The correct answer is option 'D', which means that statements 1 and 3 are correct.
1. Objective function is expressed as a linear function of variables: This means that the objective function can be represented as a linear combination of decision variables, where the coefficients of the variables are constants. For example, if we want to maximize profit, then the objective function can be represented as:
Maximize P = 10x + 20y
Where x and y are decision variables representing the quantities of two products.
2. Resources are limited: This statement is incorrect because resources are not unlimited in linear programming. In fact, the constraints of the problem represent the limited resources available.
For example, if we have a certain amount of raw material available for production, then the constraint can be represented as:
2x + 3y ≤ 500
Where x and y are decision variables representing the quantities of two products, and 500 is the limit of available raw material.
3. The decision variables are interrelated and non-negative: This statement is correct because the decision variables are related to each other and cannot be negative. In other words, the value of one variable depends on the value of other variables and all variables must have a non-negative value.
For example, if we want to minimize cost, then the constraints can be represented as:
x + y ≥ 100
2x + 3y ≥ 200
x ≥ 0, y ≥ 0
Where x and y are decision variables representing the quantities of two products, and the constraints represent the minimum production requirements and non-negativity condition.
Conclusion
Linear Programming is a powerful optimization tool that can be used to solve complex problems in various fields such as engineering, economics, and management. By formulating a problem as a linear program, we can find the optimal solution that satisfies the given constraints and objectives.
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The linear programming is used for optimization problems which satisfy the following conditions:1. Objective function is expressed as a linear function of variables.2. Resources are unlimited.3. The decision variables are interrelated and non-negative.Which of these statements is/are correct?a)1,2 and 3b)2 and 3 onlyc)1 onlyd)1 and 3 onlyCorrect answer is option 'D'. Can you explain this answer?
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The linear programming is used for optimization problems which satisfy the following conditions:1. Objective function is expressed as a linear function of variables.2. Resources are unlimited.3. The decision variables are interrelated and non-negative.Which of these statements is/are correct?a)1,2 and 3b)2 and 3 onlyc)1 onlyd)1 and 3 onlyCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The linear programming is used for optimization problems which satisfy the following conditions:1. Objective function is expressed as a linear function of variables.2. Resources are unlimited.3. The decision variables are interrelated and non-negative.Which of these statements is/are correct?a)1,2 and 3b)2 and 3 onlyc)1 onlyd)1 and 3 onlyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The linear programming is used for optimization problems which satisfy the following conditions:1. Objective function is expressed as a linear function of variables.2. Resources are unlimited.3. The decision variables are interrelated and non-negative.Which of these statements is/are correct?a)1,2 and 3b)2 and 3 onlyc)1 onlyd)1 and 3 onlyCorrect answer is option 'D'. Can you explain this answer?.
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