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Which one of the following is the correct statement? In the standard form of a linear programming problem, all constraints are
- a)Of less than or equal to type
- b)Of greater or equal to type
- c)In the form of equations
- d)Some constraints are of less than equal to type and some are of greater than equal to type
Correct answer is option 'C'. Can you explain this answer?
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Which one of the following is the correct statement? In the standard ...
**Correct Statement:**
The correct statement is option 'C': In the standard form of a linear programming problem, all constraints are in the form of equations.
**Explanation:**
Linear programming is a mathematical optimization technique used to determine the best possible outcome in a given mathematical model, given a set of constraints. The standard form of a linear programming problem involves maximizing or minimizing a linear objective function, subject to a set of linear constraints.
In the standard form, the objective function and all constraints must be in the form of equations rather than inequalities. This is because the objective function represents the quantity to be maximized or minimized, and the constraints represent the limitations or restrictions on the variables.
**Reason for Incorrect Options:**
a) Option 'A': Of less than or equal to type
This option is incorrect because linear programming problems may involve constraints of both less than or equal to and greater than or equal to type. However, in the standard form, all constraints are represented as equations.
b) Option 'B': Of greater or equal to type
This option is also incorrect for the same reason as option 'A'. Linear programming problems can have constraints of both types, but in the standard form, they are all represented as equations.
d) Option 'D': Some constraints are of less than equal to type and some are of greater than equal to type
This option is incorrect because, as mentioned earlier, in the standard form, all constraints are represented as equations and not as inequalities of any type.
**Conclusion:**
In the standard form of a linear programming problem, all constraints are represented as equations. This is because the standard form requires the objective function and constraints to be in the form of equations to ensure consistency and compatibility within the mathematical model.
The correct statement is option 'C': In the standard form of a linear programming problem, all constraints are in the form of equations.
**Explanation:**
Linear programming is a mathematical optimization technique used to determine the best possible outcome in a given mathematical model, given a set of constraints. The standard form of a linear programming problem involves maximizing or minimizing a linear objective function, subject to a set of linear constraints.
In the standard form, the objective function and all constraints must be in the form of equations rather than inequalities. This is because the objective function represents the quantity to be maximized or minimized, and the constraints represent the limitations or restrictions on the variables.
**Reason for Incorrect Options:**
a) Option 'A': Of less than or equal to type
This option is incorrect because linear programming problems may involve constraints of both less than or equal to and greater than or equal to type. However, in the standard form, all constraints are represented as equations.
b) Option 'B': Of greater or equal to type
This option is also incorrect for the same reason as option 'A'. Linear programming problems can have constraints of both types, but in the standard form, they are all represented as equations.
d) Option 'D': Some constraints are of less than equal to type and some are of greater than equal to type
This option is incorrect because, as mentioned earlier, in the standard form, all constraints are represented as equations and not as inequalities of any type.
**Conclusion:**
In the standard form of a linear programming problem, all constraints are represented as equations. This is because the standard form requires the objective function and constraints to be in the form of equations to ensure consistency and compatibility within the mathematical model.
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Which one of the following is the correct statement? In the standard form of a linear programming problem, all constraints area) Of less than or equal to typeb) Of greater or equal to typec) In the form of equationsd) Some constraints are of less than equal to type and some are of greater than equal to typeCorrect answer is option 'C'. Can you explain this answer?
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